Figure: Double-Ended BCAM. The enclosure is 91 mm × 53 mm × 41 mm, is made of anodized aluminum, and weights roughly 300 g. It contains two cameras and four red laser diodes. The lid is shown transparent so you can see inside.
The BCAM is an optical instrument designed to monitor the geometry of large structures. A single-ended BCAM contains a camera and two light sources. The camera consists of a lens and an image sensor. The light sources are red laser diodes placed on either side of the camera lens. The laser diodes have no collimating lenses, and so act as bright points of light. A double-ended BCAM contains two cameras looking in opposite directions, with two pairs of light sources.
Each BCAM uses its camera to monitor lasers on all other BCAMs in its field of view. The camera measures the position of each laser image on its image sensor. We assume that each laser lies somewhere along the line passing through its image and the camera lens. The camera is sensitive to movement across its field of view, but not to movement towards or away from the camera. The camera measures the bearing of a laser, but not its range.
The name BCAM stands for Brandeis CCD Angle Monitor, in which angle refers to the bearing measurement and CCD refers to the image sensor. A BCAM camera has relative accuracy 5 μrad within its field of view, and absolute accuracy 50 μrad with respect to its mounting plate. Its field of view is an angular cone 30 mrad × 40 mrad. At 1 m, its relative accuracy is 5 μm, its absolute accuracy is 50 μm, and its field of view is 30 mm × 40 mm. At 10 m, its relative accuracy is 50 μm, absolute accuracy is 500 μm, and its field of view is 300 mm × 400 mm.
To monitor the deformation of a large structure, we distribute BCAMs and mounting plates throughout the structure. Each mounting plate holds two or more BCAMs. Each BCAM mounts kinematically on three steel balls, and is held down by a single screw. The BCAMs on a plate do not look at one another, but instead look at BCAMs on other plates.
The balls upon which a BCAM sits define its mount coordinate system. Each BCAM camera comes with seven calibration constants: the position of its optical pivot point in mount coordinates, the bearing of its optical axis in mount coordinates, the separation of the image sensor and pivot point, and the rotation of the sensor about the optical axis. These calibration constants allow us to transform two-dimensional spot positions on the camera's image sensor into three-dimensional bearing lines in mount coordinates.
Before installation, we measure each mounting plate with a CMM (computer measuring machine), and so obtain the locations of the BCAM mounting balls in the plate coordinate system. These locations allow us to transform bearing lines from mount coordinates into plate coordinates.
Each BCAM laser comes with its own three calibration constants. These tell us the position of the laser's optical center in mount coordinates. The laser calibration allows us to determine the plate coordinates of each laser.
Each plate is now the source of many bearing lines. Each line constrains the location of a laser on another plate. Meanwhile, each plate is also the destination of many bearing lines, each of which constrains the location of one of its lasers. The combination of these constraints in our system of many plates allows us to determine the relative positions of the plates, and so deduce our global geometry.
We make sure our BCAM system provides us with many more measurements than are necessary to determine the global geometry. Because the system is over-constrained, and at the same time imperfect, there is no global geometry for which each bearing line passes exactly through its corresponding laser. Instead, we choose a global geometry that minimizes the root mean square distance between the bearing lines and their lasers. By comparing this error measure to the distance between individual bearing lines and their lasers, we can judge the performance of each camera and laser in the system. Because our system is over-constrained, we can eliminate poorly-performing cameras and lasers from our measurements, and so obtain a more accurate estimate of the global geometry without them.
Although the BCAM is conceptually simple, the task of bringing together calibration constants, image analysis results, and plate measurements to create a network of bearing lines and laser points, and then arrive at the global geometry by minimizing a global error measure, is difficult in practice. We use ARAMyS to determine our global geometry, and LWDAQ to acquire and analyze our BCAM images. We describe the application of ARAMyS and LWDAQ to a large system of BCAMs here. The paper describes a test stand consisting of thirty-six BCAMs arranged throughout a 10-m × 20-m structure. Out of the thirty-six BCAM, we rejected measurements from two cameras, and were left with absolute alignment accuracy of around 200 μm throughout the structure, and resolution of around 20 μm.
In this manual, we describe how to install BCAMs, how to interpret their measurments, how to diagnose promblems, and how to fix those problems. We pay little attention to the data acquisition hardware and software, but you can read about both in our LWDAQ User Manual. Each BCAM provides an RJ-45 socket through which we control the lasers and the CCDs, and retrieve image pixels. If you are interested in the circuits inside a BCAM, take a look at the BCAM Head (A2048) User Manual. If you would like to know how we assemble BCAMs, look at our BCAM Assembly Manual. For a detailed description and alalysis of our calibration procedure, see BCAM Calibration. For drawings and three-dimensional views of all varieties of BCAMs, go to the BCAM Home Page.
Four varieties of BCAM exist. The Black Azimuthal BCAM and the Blue Azimuthal BCAM are single-ended and mirror images of one another. They are named after the color of their anodizing and the direction we intended them to look in the cylindrical coordinates of the ATLAS mouon spectrometer. The azimuthal BCAMs are designed so that their lens and lasers are as low down towards the mounting plate as possible. They are also called low-profile BCAMs. The Black Polar BCAM and Blue Polar BCAM are double-ended and mirror images of one another. As with the azimuthal BCAMs, the polar BCAMs are named after their color and the direction we intended them to look in ATLAS. The Polar BCAMs are designed so that their lense and lasers are as highe up on their chassis as possible, so that they can be used to look up and down a corridor running through the structure they are monitoring. By placing polar BCAMs on alternate sides of such a corridor, you can monitor deformations of the corridor along an indefinate length.
Beneath each BCAM there are three depressions, a flat, a slot, and a cone. These allow the BCAM to sit kinematically on three quarter-inch (6.35-mm diameter) steel balls. We use 316 stainless steel balls because they are hard, precise, and non-magnetic.
These three mounting balls are invariably glued to an aluminum plate, which may hold several other sets of mounting balls for other BCAMs, or may be fastened to a rigid structure that holds other mounting plates, or may even be used in isolation as part of a calibration procedure. The centers of a set of three BCAM mounting balls define a mount coordinate system according to the geometric procedure we describe below.
Our calibration procedure tries to measure the direction of the camera axis to 50 μrad. A 2-μm error in the location of the slot ball with respect to the cone ball contributes a 30-μm error in the measured orientation of the BCAM on its mounting plate. In the example plate above, which calibrates a camera by sitting on a granite beam pressed up against a steel straight edge, we must measure the locations of the three balls with respect to the bottom and edge of the plate to 2 μm or better if we are to calibrate the camera axis to 50 μrad.
A BCAM camera is not an ideal thin-lens camera. It has an aperture set back from the lens and the lens's optical center does not lie upon the lens's mechanical center. Nevertheless, when it comes to relating the position of laser images on the image sensor to the location of the lasers themselves, the camera is equivalent to a virtual thin-lens camera, as we prove here.
When we calibrate a BCAM camera, we determine the properties of its equivalent thin-lens camera with respect to its kinematic mounting balls. We measure the location of the lens center, or pivot point to 20 μm in the transverse directions, and 1 mm in the direction of the camera's axis. We measure the direction of the camera axis to 50 μrad, the distance to the image sensor to 100 μm, and the rotation of the sensor to 1 mrad.
The BCAM lasers are not perfect points of light. Their light-emitting surfaces measure roughly 20 μm × 50 μm. Nevertheless, they are equivalent to a virtual point source of light. When we calibrate BCAM lasers, we measure the location of this equivalent point source with respect to the mounting balls to better than 10 μm.
All existing BCAMs use the TC255P image sensor. The TC255P's active area is 3.2 mm × 2.4 mm, with 10-μm square pixels. The camera lense is 75 mm from the sensor, so the field of view of the camera is 43 mrad × 32 mrad, which is 43 cm by 32 cm at a range of 10 m. We usually quote the field of view as 40 mrad × 30 mrad.
A laser suitable for use in a BCAM is the LDP65001E laser from Lumex. The LDP650001E emits a cone of ruby-red light. If you hold a piece of white paper 100 mm in front of the laser package, it shines a bright stripe of light on the paper roughly 75 mm by 25 mm.
All our existing BCAMs use a plano-convex lens of focal length 72 mm, a 2-mm aperture, and a TC255P CCD (charge-coupled device) image sensor. The image sensor provides an array of 344 by 244 pixels. Each pixel is 10 μm square.
Because the camera aperture is offset from the lens, and the optical center of the lens is never exactly coincident with its physical center, the camera is not a thin lens optical system. Nevertheless, it has a thin lens equivalent, consisting of a virtual perfect thin lens and a virtual CCD, as we show in BCAM Calibration. The pivot point of a BCAM camera is the center of its virtual perfect thin lens, and its camera axis is the line joining the center of this lens and the center of the virtual CCD. The images we obtain from the real CCD are exactly the same as the images we would obtain from the CCD in the virtual system.
Once we obtain an image of lasers point sources, we determine the locations of the point sources within the image. We draw a rectangle around each spot, just large enough to enclose all its pixels. Within each rectangle, we determine the center of the spot using a weighted sum with threshold (as we describe below). The weighted sum has resolution better than 0.5 μm, or 5% of a pixel width.
We control and read out our BCAMs with our Long-Wire Data Acquisition (LWDAQ) system. Each BCAM has its own electronics. The Polar BCAM contains our Polar BCAM Head (A2051), and the Azimuthal BCAM contains our Azimuthal BCAM Head (A2048). We describe how to use the LWDAQ hardware and software in the LWDAQ User Manual. Each BCAM connects to the LWDAQ with a CAT-5 network cable. If you wish to connect dozens of BCAMs to the LWDAQ, you will find a multiplexer useful, such as our LWDAQ Multiplexer (A2046). You will certainly need a LWDAQ Driver, such as the LWDAQ Driver with Ethernet Interface A2037E. The LWDAQ is available for free, and runs on Mac OS X, Windows, Linux, and UNIX. The software communicates over TCP/IP with the LWDAQ Driver. You can connect the LWDAQ Driver directly to the ethernet socket in your computer, or you can connect it to the internet.
Suppose we fix a camera rigidly to the ground at night and photograph a star. The star appears in our photograph as a point of light. We have a photograph of the star, and we can measure where the star lies within the field of view of our camera, but the photograph alone tells us nothing about the position of the star with respect to the earth. Nevertheless, movements within the camera's field of view do correspond to changes in the altitude and azimuth of the star. Altitude and azimuth map exactly onto an orthogonal coordinate system in the photograph. If only we knew the offset, orientation, and scale of this coordinate system with respect to the plane of the photograph, we could translate the position of image into the bearing of the star. The task of determining the relationship between the bearing of the star and the position of its image is the task of calibrating the camera. In this case, we have the task of determining four calibration constants. These are the bearing that corresponds to the center of the photograph (two constants), the rotation of the bearing coordinates with respect to the photographic coordinates (one constant), and a scaling factor relating the size of displacements in the two systems (the fourth constant).
A BCAM camera operates in the same way, with the laser light sources instead of stars, and a local coordinate system defined by its kinematic mounting balls instead of by the vertical and northerly directions. Unlike stars, however, BCAM light sources are not infinitely far away, so that the bearing of a light source with respect to a BCAM depends not only upon the orientation of the BCAM, but also upon its location. We define the BCAM source bearing as the bearing of the source point with respect to the camera's pivot point. A source bearing maps directly onto the camera's CCD in the same way that a star's bearing maps directly onto an astronomical photograph.
If we move an astronomical camera any significant distance across the surface of the Earth, and orient it as we did before with respect to the vertical and northerly directions, then we will find that the image of our star has moved. This movement is due to the curvature of the Earth, and also the time it takes us to move our camera, during which the Earth rotates. If we want to predict the bearing of a star in one location given its bearing in another, we need to know the relative orientation of the vertical and northerly directions in the two locations. We can determine this relative orientation by comparing the latitude and longitude of the two locations. When we have finished our calculation, we have two numbers that specify the orientation of one location with respect to the vertical and northerly directions of the other.
BCAM users, unlike astronomers, do not have to contend with the curvature of the earth. Nevertheless, if we are to combine the measurements made by two BCAMs into a more comprehensive measurement of the geometry of a structure, we must know the relative orientations of their mounting coordinates. Not only that, we must know the relative positions of their mounting coordinates, because BCAM sources, unlike stars, are not infinitely far away. One way to make sure we know the relative orientations and positions of two mount coordinate systems is to put both mounts on the same rigid plate, and measure the positions of the mounting balls. Another is to place many mounts upon a long flexible structure, measure their relative positions, and then monitor the shape of this flexible structure so as to determine any changes in the relative positions of the mounts. The alignment bars we designed for the ATLAS end-cap muon alignment system are examples of such flexible structures. The longest are aluminum tubes 9.6 m long and 85 mm in diameter.
A large BCAM system might consist of hundreds of BCAMs mounted upon a large structure, plus hundreds more mounted in groups upon rigid plates and flexible reference structures. The measurements of all BCAMs combined provides us with the geometry of the large structure in a single, global coordinate system. The measurements made by the BCAMs are similar to those made by theodolites, and combining their measurements is akin to triangulation. Unlike theodolites, however, BCAMs take their measurements quickly and automatically. A BCAM system provides a real-time picture of the shape of a large structure. BCAMs are small enough to be inserted into small spaces, and to look down narrow corridors.
Each BCAM provides two light sources. The laser pairs in the BCAMs of Figures 1 and 2 are separated by 16 mm. A BCAM camera looking at these lasers can measure their range by measuring their angular separation. If the angular separation of the two lasers is ten milliradians, the lasers are 1.6 m away.
The principle technique we use to calibrate both cameras and sources is to mount the camera in a roll cage and rotate it by 360° in 90° steps. We know the positions of the mounting balls with respect to the base plate in all four roll cage orientations, which gives us the relative orientation and position of the mount coordinates. While the BCAM rotates in the roll cage, its camera sees four lasers in a calibrated source block. We take images of the lasers in the source block at two different ranges and from all four orientations. From the thirty-two images we obtain thirty-two image positions, and from these thirty-two image positions we obtain, with ample redundancy, the seven calibration parameters of the camera.
When we calibrate BCAM sources, we mount them in the roll cage and take pictures of them in the four orientations using the camera in another BCAM mounted in front of the roll cage. From the eight images we obtain eight image positions, and from these eight image positions we obtain, with amble redundancy, the positions of both sources.
As we mentioned above, the centers of the steel balls in a kinematic BCAM mount define our mount coordinate system. When we calibrate a BCAM camera, one of the constants we obtain is the position of its pivot point. We specify this position in mount coordinates. The nominal positions of the balls in a kinematic mount are given by the mount drawing. We intend the BCAM to be tolerant of balls that are up to 250 μm away from their nominal positions. If our calibrated pivot point position is indeed to be a constant property of a BCAM from one kinematic mount to the next, then we must define our mount coordinates in such a way that the location and orientation of the mount coordinates is constant with respect to the body of the BCAM for all kinematic mounts.
We define mount coordinates is as follows. The center of the cone ball is the origin. The cross product of the slot-cone and flat-cone vectors defines the y-axis. The z-axis lies in the plane of the three balls, and subtends a fixed angle of 0.2798 radians (16.031 degrees) with the slot-cone line. If the mounting balls are in their nominal positions exactly, then the z-axis bisects the angle subtended by the slot and flat at the cone, and points straight forward out of the BCAM, parallel to the sides of the chassis. The x-axis completes a right-angled coordinate system with the y- and z-axes.
The y-axis of the mount coordinates for our black polar BCAM and black azimuthal BCAM both point up from the base of the BCAM to the top of the BCAM. But in our blue polar BCAM and blue azimuthal BCAM, the chassis is a mirror image of the black chassis, so that the slot and flat balls are swapped. Consequently, the y-axis in a blue BCAM points downwards.
With the mount coordinates defined as we have just described, the origin lies in the same place from one mount to the next provided that the diameters of the cone balls in each mount are the same. The absolute diameter of the kinematic mounting balls should be 6.35 inches ±10 m. These are tight tolerances, but precision steel balls are inexpensive and readily available.
The orientations of the mount coordinates with respect to the BCAM chassis will be fixed provided the slot under the BCAM points exactly at the cone, the flat is perfectly flat, and the balls have the same diameter. The variation between the diameters of the mounting balls should be ±2 μm. The accuracy of the slot and flat restrict the total deviation of the kinematic mounting balls from their nominal positions. As we mentioned above, we can tolerate no more than ±250 μm deviation from the nominal ball positions.
Here are the calibration constants of a black polar BCAM camera, all on one line:
12.747 35.282 3.705 2.115 -5.303 1 76.124 12.921
The first three numbers are the x, y, and z mount coordinates of the camera pivot point, in millimeters. The next two numbers are the direction cosines of the camera axis direction, x and y components respectively, in milliradians. We try to make our BCAMs so that the axis direction lies within ±5 mrad of the z-axis. The sixth number is the z-direction of the camera axis. This is -1 for the rear-facing camera in a double-ended polar BCAM. The seventh number is the distance backwards along the camera axis from the pivot point to the surface of the CCD, in millimeters. The final number is the rotation of the CCD about the z-axis in milliradians. Positive rotation is when we rotate the CCD clockwise while facing in the positive z-direction.
Here are the calibration constants from a blue azimuthal BCAM.
-12.677 -13.069 0.922 -2.249 -1.498 1 75.137 5.902
As you can see, the x and y coordinates of the pivot point position are both negative. The y-coordinate points downwards on the blue BCAM, but and the x-coordinate points the opposite direction from that of the black BCAM x-axis. Because the pivot point is on the other side of the cone ball in the blue BCAM, its x-coordinate is also negative. The distance from the pivot point to the CCD is still positive, because we define this as positive when we move back along the camera axis to the CCD, not when we move in any particular direction along the z-axis.
Here is the full output from our calibration program for the same blue azimuthal BCAM.
Calibration Constants for Front-Facing Camera on Device 20MABNDB000025:
-----------------------------------------------------------------------
| Pivot Position | Axis Direction | CCD | CCD
|-----------------------|-------------------| -to- | Rot-
| x | y | z | x | y | | Pivot | ation
Pair | (mm) | (mm) | (mm) | (mrad)| (mrad)| z | (mm) | (mrad)
-----------------------------------------------------------------------
1_2 -12.653 -13.078 0.698 -2.265 -1.497 1 75.143 5.795
1_3 -12.684 -13.080 1.194 -2.227 -1.506 1 75.106 6.033
1_4 -12.688 -13.076 1.306 -2.280 -1.500 1 75.116 6.014
2_3 -12.686 -13.048 0.539 -2.232 -1.545 1 75.158 5.790
2_4 -12.670 -13.059 0.651 -2.271 -1.491 1 75.169 5.771
3_4 -12.679 -13.075 1.147 -2.219 -1.452 1 75.131 6.010
-----------------------------------------------------------------------
average -12.677 -13.069 0.922 -2.249 -1.498 1 75.137 5.902
spread 0.036 0.032 0.767 0.061 0.093 0 0.063 0.262
limit 0.080 0.080 4.000 0.100 0.100 0 0.300 1.000
-----------------------------------------------------------------------
Calibration performed at time 20031031160639
We get six pairs of roll cage orientations from our four orientations, and each pair gives us a set of calibration constants. We check the spread in calibration constants across these six pairs of orientations to see if anything went wrong while we were taking measurements and moving the calibration pieces. The final calibration constants we provide for each BCAM are the average of the six values.
Here are the source calibration constants for the same camera.
Calibration Constants for Front Sources on Device 20MABNDB000025:
-------------------------------------------------
| Inner Source | Outer Source |
|-----------------------|-------|
| x | y | x | y | z
Pair | (mm) | (mm) | (mm) | (mm) | (mm)
-------------------------------------------------
1_2 -20.644 -13.088 -4.634 -13.051 0.360
1_3 -20.647 -13.083 -4.655 -13.050 0.360
1_4 -20.639 -13.066 -4.639 -13.051 0.360
2_3 -20.642 -13.079 -4.654 -13.029 0.360
2_4 -20.630 -13.079 -4.636 -13.048 0.360
3_4 -20.631 -13.091 -4.655 -13.066 0.360
-------------------------------------------------
average -20.639 -13.081 -4.646 -13.049 0.360
spread 0.017 0.025 0.022 0.037 0.000
limit 0.040 0.040 0.040 0.040 0.040
-------------------------------------------------
Calibration performed at time 20031031115752
The source positions are the centers of the transmitting facets of the lasers. We give the x and y coordinates of each laser, and then its nominal z-position. Our calibration procedure does not measure the z-position of the lasers, but we know by construction where they are to within ±50 um.
The coordinate system defined by a BCAM's three mounting balls are its mount coordinates. We define mount coordinates above. Mount coordinates are such that they have the same location and orientaion with respect to a BCAM despite small variations in the relative positions of the three mounting balls from one BCAM mount to the next.
The BCAM Instrument in our LWDAQ software returns spot positions on the image sensor. You can apply the BCAM analysis to an image of your own with the LWDAQ library command lwdaq_bcam. We describe the spot-finding analysis routine in more detail below. For now, we will concentrate upon its main result, which is the spot positions in image coordinates. The following figure shows how image coordinates relate to the image sensor area and mount coordinates.
The diagram does not show the kinematic mounts beneath the BCAMs, but the figure above does. Looking at the diagram, the flat is at the rear right in the black BCAMs, and at the rear left in the blue BCAMs. In all cases, the flat is in the positive mount-coordinate x-direction with respect to the slot.
To obtain a line in global coordinates from a BCAM measurement position, we combine the BCAM's calibration constants in mount coordinates, the spot position in image coordinates, and the mounting ball positions in global coordinates.
First we transform the two-dimensional image-coordinate spot position into a three-dimensional mount-coordinate spot position. Our calibration constants tell us the bearing of the line joining the center of the CCD and the camera pivot point. The center of the CCD is not the image coordinate origin. It is a point in image coordinates we pick in our definition of image coordinates. Our definition is buried within our BCAM calibration code, bcam.pas.
const
bcam_ccd_center_x=1.720;{along ccd x-axis (mm)}
bcam_ccd_center_y=1.220;{along ccd y-axis (mm)}
Our routine for converting between image coordinates and mount coordinates is as follows. Note that our code refers to mount coordinates as bcam coordinates. The routine uses all the calibration constants in its calculation.
{
ccd_center calculates the bcam coordinates of the ccd center.
}
function ccd_center(camera:bcam_camera_type):xyz_point_type;
begin
with camera do
ccd_center:=xyz_sum(pivot,xyz_scale(axis,-ccd_to_pivot));
end;
{
bcam_from_image_point converts a point in the image into
a point in bcam coordinates. The calculation takes account
of the orientation of the ccd in the camera.
}
function bcam_from_image_point(p:xy_point_type;
camera:bcam_camera_type):xyz_point_type;
var
q:xy_point_type;
r:xyz_point_type;
cc:xyz_point_type;
begin
q.x:=p.x-bcam_ccd_center_x;
q.y:=p.y-bcam_ccd_center_y;
cc:=ccd_center(camera);
with camera do begin
if axis.z>0 then begin
r.x:=cc.x+q.x*cos(ccd_rotation)-q.y*sin(ccd_rotation);
r.y:=cc.y+q.y*cos(ccd_rotation)+q.x*sin(ccd_rotation);
end
else begin
r.x:=cc.x-q.x*cos(ccd_rotation)+q.y*sin(ccd_rotation);
r.y:=cc.y+q.y*cos(ccd_rotation)+q.x*sin(ccd_rotation);
end;
r.z:=cc.z;
end;
bcam_from_image_point:=r;
end;
Once we have the spot position in mount coordinates, we define a line in mount coordinates using our spot position and the calibrated pivot point position. We transform this line from mount coordinates into global coordinates using the global coordinates of the mounting balls. The global_from_bcam_line does this job in our code.
You don't have to compile and call our Pascal code to have access to these routines. We provide access to them for you through the LWDAQ software's TCL/TK interpreter. You can transform a spot position into a mount coordinate line using bcam_source_bearing. If you know the range of a light source, you can determine its position in mount coordinates in one jump using bcam_source_position. You can transform from mount to global coordinates with global_from_bcam_point. If you want to predict the location of spots on the CCD, you can use bcam_from_global_point. We use these routine in our graninte beam calibration script, which we used to calibrate BCAMs on a granite beam with a straight edge, instead of with our roll cage.
Let us first consider the accuracy with which a BCAM can track changes in the source bearing or measure the angular separation of two sources. The angular resolution of a BCAM camera 5 μrad or better at all ranges. Its resolution when measuring a small angular separation is therefore 7 μrad. If we want to measurement of a large angular separation, we must rely upon the accuracy of scaling factor that relates the angular separation of source points to the separation of their images on the CCD. This scaling factor is represented in our camera calibration constants as the distance between the pivot point and the CCD. Our camera calibration gives us this distance to better than one part in a thousand (0.1%). If the angular separation of two sources is 10 mrad, our accuracy is 10 μrad, and our resolution is 7 μrad.
Now let us consider how well the BCAM can measure the co-linearity of three points. We have a camera at one of the extreme points looking at sources at the other two points. We measure the size of the angular separation of these sources with resolution 7 μrad and accuracy 0.1%. But there are other sources of error in our co-linearity measurement. To make sense of our angular measurements, we must also know the location of the camera pivot point with respect to its mount, and the locations of the two light sources with respect to their mounts. Then we can say that we are measuring the co-linearity of the three mounts. The co-linearity measurement therefore depends upon the accuracy with which we know the position of the pivot point in the directions perpendicular to the camera axis, and the positions of the sources in the same directions. Our calibration tells us the pivot point position to better than 20 μm in the directions perpendicular to the camera axis, and the source positions to better than 10 μm.
Our camera calibration tells us the direction of each camera axis to better than 50 μrad with respect to its mount coordinates. Suppose we have two BCAMs on a rigid plate looking at two separate light sources. We have measured the plate exactly. We can now measure the angle subtended by the two light sources at some point on the plate close to the BCAMs. We measure the bearing of each source with respect to the pivot point of the camera that views it, and translate this bearing into a line in the coordinate system of the plate. The direction of each line will be correct to 50 urad. We can therefore determine the angular separation of the two sources at a point in the plate to an accuracy of approximately 70 μrad.
Another measurement we can perform with the BCAM is the range measurement we described above. Our source calibration measures the separation of two laser on a BCAM to better than 10 μm, or 0.06%. Our camera calibration measures the location of the camera pivot point along the camera axis to better than 500 μm. Each camera can measure the angular separation of two lasers on another BCAM to better than 7 μrad. Consequently, at a range 2 m, we can measure the absolute range of another BCAM with accuracy 2 mm, and at 10 m our accuracy is 50 mm.
The BCAM sits upon three quarter-inch (6.35-mm diameter) steel balls. We hold it in place with a single M4 screw (4-mm diameter shaft, 0.8-mm threads). The Polar BCAM takes a 50-mm M4, and the Azimuthal BCAM takes a 40-mm M4. We recommend a hex head screw because it gives us better control when tightening the screw. If we tighten the screw too much, the ball beneath the flat depression of the kinematic mount will bite deeply into the flat, and we will rotate the BCAM with respect to the position in which we calibrated it. The depth to which the mounting ball bites into the flat is proportional to the tension in the screw. The tension in the screw is proportional to the deformation of the BCAM lid beneath the screw head. The lid of the BCAM acts like a spring, moderating the force with which the enclosure is held to the mounting balls.
To secure the BCAM accurately, we insert an Allen key in the head of the mounting screw and tighten the screw by rotating the vertical shaft of the Allen key with our finger and thumb. The screw is now finger-tight. Once the screw is finger-tight, we tighten it by one more half-turn, which pushes the lid down by 400 μm. The resulting indentation made in the flat depression by its mounting ball is roughly 300 μm in diameter, which means it is a few microns deep. As we force the BCAM down on onto the flat depression's ball, the BCAM chassis rotates about the line joining the cone and slot balls. This rotation has two effects upon our calibration constants. The CCD rotates about the camera axis, and the camera axis itself tilts upwards. We measured these two effects when we calibrated BCAMs on a granite beam, as we describe here. On the granite beam, we can calibrate a BCAM without screwing it to its base, but instead by holding it down with two other BCAMs acting as weights. We found that tightening the screw to finger-tight plus half a turn tilted the axis.y up by 20 μrad, and rotated the CCD by roughly 50 μrad.
When we asked five different members of our group to follow our "finger-tight plus half-turn" mounting instructions ten times, and each time we measured the bearing of a light source five meters away. The standard deviation of this bearing was 10 μrad. We concluded that the mounting force was consistent to within 10%.
Nevertheless, if we tighten the mounting screw by another half-turn, the BCAM will rotate by another 20 μrad in axis.y. Furthermore, when we over-tighten the screw by a half-turn, we make a 500-μm diameter depression in the flat surface that is 20 μm deep. We can loosen the screw by half a turn, but this depression will not go away. The BCAM will always mount incorrectly on this particular ball triplet and any other ball triplet that brings the flat ball into the 20-μm depression.
Nowadays, we use torque screw drivers to tighten BCAM screws in our laboratory. We tighten the screw to "twenty ounce-inches", which is 0.14 Nm. This torque is close to that we obtain with our figher-tight plus half-turn rule. If we ignore friction between the screw and the lid, we see that this 0.14 Nm acting on the 0.8-mm threads generates a downward force of 1000 N, which would be like placing a 100-kg weight on the BCAM. But the force the screw generates in practice is far less than this. We can raise the BCAM up off its balls, while it is screwed down, by exerting a force of no more than 100 N. We conclude that friction between the screw and the lid play a critical role in moderating the fastening force, and we rely upon the consistency of this friction for the consistency of our mounting procedure.
Be sure to follow our finger-tight plus half-turn rule or use a torque screw driver set to 0.14 Nm when you fasten BCAMs to their mounts.. Over-tightening the mounting screw will damage the BCAM. Both over-tightening and under-tightening will change both the CCD rotation and axis direction of the BCAM's cameras. The calibration constants we provide apply to BCAMs secured to their mounts according to the finger-tight plus half-turn rule.
A BCAM image is a photograph taken by a BCAM camera of one or more BCAM lasers. The simplest BCAM image capture procedure is as follows.
Background-subtraction image capture procedure is as follows.
Our data acquisition software uses the LWDAQ to digitize BCAM images with eight-bit resolution. The pixel intensities range from zero to 255. When we subtract the background image, we may find that the result is slightly negative. Our electronically-generated image noise is a fraction of an ADC counts rms, but when there are sudden changes in the ambient light intensity, the background might be several counts brighter in places than the laser image. In some cases, with unshielded cables or damaged electronic circuits, we have observed noise spikes several counts high. Because we store these images as arrays of bytes in memory, the value −1 will be recorded as 255. Our analysis program simply sets negative values to zero.
Background subtraction does require us to capture two images from the BCAM, which doubles your data acquisition time. In our laboratory, we rarely use background subtraction, because we have no sunlight to worry about, and we like the data acquisition to be fast.
Whether an image is background-subtracted or not, we must check to make sure that its peak intensity lies within an acceptable range before we analyze the image to find the locations of its laser spots. We will talk more about the acceptable range of image intensities later, but for now, let us assume that we wish to capture a BCAM image with a peak intensity that lies between 100 and 140 counts above the average intensity in the image. If the peak intensity is too high, we must reduce the time for which we flash the laser, which we call the exposure time. Conversely, if the peak intensity is too low, we must increase the exposure time.
There are several other properties of the image we can check to make sure our image is useful and accurate. The figure below shows an example quality assurance procedure.
The light spots in most images take up only a small part of the entire CCD. If we want to see what lies within the field of view, perhaps to determine whether our BCAM camera is facing in the right direction, we can capture an ambient image with a slightly different, and simpler, procedure.
The 100 ms of step (2) is the ambient-light exposure time. Here is an example ambient-light image.
You will notice the black band on the left side of the image. This band is made up of eighteen black columns. The first six of these columns are added to the image by our data acquisition hardware. The remaining twelve are black-level reference columns in the CCD. The black-level are like any other columns in the image, except they are kept in the dark by a layer of aluminum. As you can see, the blue analysis boundary of Figures 4 and 5 excludes the first eighteen columns of the image.
An ambient-light image requires ambient light. If there is no ambient light, you can try to make your own by flashing one or both of the lasers on the BCAM that is taking the ambient-light picture. You might see something in the reflected light of the lasers. Unfortunately, because the lasers emit highly coherent light, an image obtained with their illumination will be plagued with bright and dark spots, or laser speckle.
You will find an example background-subtracted image above. If you would like to experiment with the BCAM software, you can use our demonstration stand to capture BCAM images.
The standard deviation of intensity in this image is only four ADC counts. To display this image clearly, we intensified it. Our display programs provide three grades of intensification, each of which comes into its own for particular images. We will be glad to supply you with our intensification source code. We use exact intensification with images like this. Exact intensification shows the brightest spot in the analysis boundary as white, and the darkest spot as black. We have two other varieties of intensification, each of which uses the standard deviation of the image intensity within the analysis boundary, which we call the image amplitude, and the average intensity, which we call the image background to determine the display intensity. We displayed the ambient-light image above with mild intensification. With mild intensification, any pixel with intensity five or more amplitudes above the background appears white, and any pixel five or more amplitudes below background is black. With strong intensification we do the same, except with a limit of two amplitudes above and below the background.
Ambient illumination is rarely a problem with BCAM cameras, because the field of view is so small and the lasers are so bright. But there are times when it is a problem, especially when sunlight is reflecting into the BCAM field of view, as shown in below.
When an ambient light or a reflection of ambient light does appear in the field of view, our analysis program cannot distinguish between the laser and the reflection. If there is a steady gradient to the ambient illumination across the field of view, the apparent position of the laser image will be displaced in the direction of the gradient.
We can remove ambient light from our final image, so long as it is the ambient light is not so bright as to saturate our image sensor. We capture two separate images, one with the lasers flashing, and the other with the lasers off. The second image is our background image. We subtract the background from the image we take with the lasers flashing, to obtain our final image. We call this procedure background subtraction, and we use it whenever we have problems with ambient light.
Ambient light is one source of confusion in BCAM images. We can remove it by background subtraction. Reflections of the lasers of shiny surfaces within the BCAM's field of view are another. Unlike ambient light, reflections of the lasers cannot be removed from our final image by background subtraction. The refelections are present if and only if the lasers are flashing. The brighter the lasers, the brighter the reflections.
One thing we can say about reflections is that they will never be brighter than the laser itself. We distinguish between reflections and real laser images by identifying all the separate spots in the image and then sorting them in order of descending brightness. The brightest spots are the lasers. The dimmest spots are either reflections or noise. We describe our multi-spot analysis in more detail below.
Suppose we cover our BCAM with a black cloth and take an ambient-light image with a zero-second exposure time. The amplitude of this image is what we call the image noise. You can learn more about the nature of the noise in an image by displaying the blank image with intensification. You should see randomly-scattered points of bright and dark, with image amplitude between 0.1 and 1.0 ADC counts, depending upon the length of your cables and their environment. In theory, when we digitize an image pixel with our eight-bit ADC, we introduce quantization noise of 0.3 counts rms. But if the image has uniform intensity, the quantization is smaller. The noise in our laboratory images is usually 0.2 counts, even with long cables coiled upon the floor. But the image noise in large data acquisition systems with long cables, such as ATLAS or ALICE, can be as high as 1.0 counts.
You might see noise that is not random, as in the image above. Diagonal noise can be caused by switching power supplies.. In our experience, the intensity of diagonal noise is never more than 1 count, and has no significant affect upon the performance of a BCAM.
Far worse than diagonal noise are noise spikes. These appear as white and black pixels distributed randomly in the image. If their height is always less than ten or twenty counts, they are probably the result of damaged electronics in the BCAM camera or of a faulty cable. If their height ranges from one to one hundred counts, they are probably the result of noisy transmission between the LWDAQ driver and your data acquisition computer. Small noise spikes you can overcome, if you have to, by raising the analysis threshold. Large noise spikes make image analysis impossible. In either case, the noise spikes indicate that something is wrong with your data acquisition hardware.
Our advertised 5-μrad source bearing resolution, requires us to measure the position of point source images with resolution 400 nm on the image sensor. (The CCD is 75 mm from the pivot point, and 75 mm multiplied by 5 μrad is 375 nm.) In the Polar or Azimuthal BCAMs, this 400 nm is 4% of a pixel width. When the source is three meters from the BCAM, the image is only four pixels wide, so 400-nm is 1% of the image width.
The LWDAQ provides images with electronic noise less than 0.1% of the image intensity. Even the smallest images spread their light over twenty or thirty pixels, so when we calculate the light centroid we average the electronic noise over twenty or thirty pixels. It is not at first obvious that we can determine the position of a light spot to better than 4% of a pixel width. Nevertheless, with a simple weighted-centroid calculation, we can obtain 4% resolution or better, even with pixels that span only four pixels.
The BCAM Instrument captures BCAM images and analyzes them. It gives you a choice between single-spot or multi-spot analysis. In single-spot analysis, it assumes that there is only one spot, and we use every pixel in the analysis boundaries to determine its centroid. In multi-spot analysis, it identifies connected groups of pixels above threshold, enclose each such group in a rectangle, and calculate its centroid using only the pixels within this rectangle.
If you look in the image above, or in images you take from our demonstration stand, you will see a blue rectangle that marks the analysis boundaries. We set the analysis boundaries to include however much of the image we want to use. The BCAM rejects spots outside the boundaries. Its multi-sppot analysis returns a list of spots sorted in order of descending brightness. By flashing one laser in the field of view, and choosing the brightest spot returned by the analysis, the BCAM allows you to reject reflections and noise.
If you want to look at our BCAM image analysis code, you will find it here. The code is in Pascal, and compiles with the GNU Pascal Compiler.
Our centroid-calculating routine subtracts a threshold from the intensity of each pixel associated with a spot, and calculates the weighted sum of the spot intensity after subtraction. Any pixel whose intensity is negative after subtracting the threshold we eliminate from the sum, by setting its intensity to zero. We recommend a threshold a few counts above the average image intensity, or that you calculate the threshold by examining the intensity of the image. We obtain robust and accurate analysis by taking the average and maximum intensities in the image, and picking a threshold that is 10% of the way from the average to the maximum. The BCAM Instrument allows you to instruct the BCAM Instrument to perform this threshold determination automatically.
Here is the result of BCAM image analysis on the image shown above.
BCAM_1 2697.50 1413.94 22 210 0.003 58 1694.20 1401.24 26 202 0.001 58
The first two numbers are the position of the brightest spot, given in microns in image coordinates. The third number (22) is the number of pixels above threshold in the spot. The fourth number (210) is the total above-threshold brightness of all these pixels. The fifth number (0.003) is the change in spot position for a one-count increase in threshold. The sixth number (58) is the threshold used. The final six numbers have the same meaning, but apply to the second brightest spot in the image.
For more information on how to use the BCAM Instrument, see the LWDAQ User Manual.
The Polar and Azimuthal BCAM cameras are in sharp focus at around 3 m. The size and shape of the laser images we see at range 3 m are a function of the optics of the camera only. With perfect optics and a wider aperture, the image of a laser at 3 m would be a spot on the CCD only a few microns wide. But diffraction at the 2-mm aperture of the BCAM camera spreads the light spot until it covers several pixels, even when the image is in perfect focus.
We can imagine rays passing through the aperture each spreading out into a cone. The sharp tip of the cone is at the aperture. The angle inside the sharp tip of the cone, in radians, is roughly equal to the wavelength of the light divided by the aperture diameter. Our laser wavelength is 650 nm and the aperture is 2 mm, so the diffraction angle is approximately 300 μrad. Over the 75-mm distance between the lens and the CCD, this 300 μrad creates an image 24 μm in diameter, or 2.5 pixels.
At shorter ranges, the laser image slowly grows as it becomes defocused. At around 60 cm, depending upon the BCAM, a black hole appears in the middle of the image. The black hole is the result of destructive interference at the center of the image. If we use incoherent, flat-topped infra-red light-emitting diodes as a light sources, we still see the same hole in the image, so the hole is not a consequence of using a laser light source.
At longer ranges, the spot spreads out a little, but images at ranges greater than ten meters all look the same. The only upper limit to the BCAM range is the camera exposure time required to obtain a clear image.
We adjust the lenses of our Polar and Azimuthal BCAMs until a laser at range three meters has the smallest possible image diameter. Three meters is our focal range. We can reduce the focal range by placing the lens farther from the CCD. If we move the focal range to 1.5 m, images at 60 cm no longer show a black hole in the middle. But images at rangers greater than eight meters will become sharply pointed in the middle, with a dark ring around them, and then a shadowy ring farther out, as you can see below.
The ten-meter image above looks okay, but it is not, as we describe at length in BCAM Focus. There is a thin, dark circle of destructive interference around the bright center of the image spot. This dark circle is so thin that we cannot see it with our 10-μm pixels. If we move the light spot across the CCD in uniform steps, we see cyclic non-linearity in our measurement of the image position. We believe these cycles are caused by regular features on the CCD interacting with the thin, dark circle. Such non-linearity at long ranges introduces large errors in our BCAM measurements. The focal range of the BCAM is therefore 3 m so that the images at long ranges perform well. Images at short ranges, such as 50 cm, perform less well, but errors on the CCD are proportionally less significant at short ranges. A 1-μm error on the CCD represents a 13-μrad error in source bearing. At 10 m, this error represents 130 μm in the position of the laser, but at 50 cm it represents an error of only 7 μm.
The graph below shows the number of pixels above threshold in the focused spot verses lens position at range 1.3 m.
Focus at range 1.3 m is important during calibration, where 1.3 m is the closer of two ranges at which we make our calibration measurements. The BCAM spot at range 1.3 m should be sharp enough to give us better than 0.5 μm resolution in measurement of its position. At the same time, we do not want perfect focus at 1.3 m, because this would spoil the quality of the image at long ranges. With this particular lens, we choose to position 1.2 mm, which allows for ±0.2 mm error in placement while still maintaining the spot quality at short and long ranges.
The variation in focal length from one lens to the next in a batch of lenses might be 1%. With our 72-mm focal length 6-mm diameter lenses (NT32-851 from Edmund Optics) we find that the focal length of lenses within a batch of several hundred are all within less than 1%, so we can use the same lens position for all lenses from the same batch. But we still test the focal length of new batches of lenses.
One measure of the quality of a BCAM image is a graph of the calculated spot position against analysis threshold.
When we analyze images, we can make sure that the threshold we use is always the same. But if the intensity of the image changes from one image to the next, the value of the threshold as a percentage of the image intensity does change.
Plots of centroid offset verses threshold, such as those in Figures 8 and 9, tell us how sensitive we are to the intensity of the light spot. In these two plots, the spot intensity was 115 counts above the background inensity. We varied the threshold from five to fifty-five counts above the background, so that the threshold varied from 5% to 50% of the intensity of the spot above the background. Over this range, the image position we calculated changed by 0.5 μm. In terms of source bearing, 0.5 μm is 7 μrad.
In theory, the lower the threshold, the more accurate the BCAM. In practice, noise in the image forces us to raise the threshold to a few counts above the background intensity. Furthermore, we often see reflections of the target laser on shiny surfaces within the camera's field of view. These reflections are far less bright than the laser itself. You will see them only if you intensify your background-subtracted image with a procedure similar our mild or strong intensification, but not our exact intensification. To exclude reflections from your image analysis, you can raise the analysis threshold until it is above the intensity of the reflection. But our multiple-spot analysis routine, which is available in the BCAM Instrument of our LWDAQ Software separates the spots in an image and sorts them in descending order of brightness. By this means, you can always eliminate reflections, and you do not have to worry about them disturbing your measurements.
We recommend a threshold of ten counts if you perform background subtraction, or ten percent of the way from the average intensity of the image to the maximum intensity if you do not perform background subtraction.
The following graph shows how the resolution of a BCAM camera varies with image intensity at ranges 1 m and 10 m.
The graph shows how atmospheric turbulence dominates the BCAM's resolution at range 10 m, provided the image intensity is greater than around 50 counts. For intensities higher than 50 counts, the resolution remains roughly constant at 0.5 μm. At range 1 m, atmospheric effects are insignificant compared to electronic noise. Resolution steadily improves with intensity, reaching 0.1 μm for intensity 190 counts.
We obtained both our graphs with cables shorter than 20 m. With 130-m cables, electronic noise increases from around 0.2 counts to 1 count. With five times the noise, we benefit from a brighter image.
In general, therefore, we can expect better resolution with brighter images. As we make our images brighter, however, we must be careful that pixels in the center of our light spot do not saturate. If they saturate, we will get large measurement errors, especially in the vertical direction, which is the direction in which excess pixel charge tends to leak. And so we must concern ourselves with the exposure time of our image, which includes both the length of time for which we flash the lasers, but also the length of time for which the image sensor is exposed to ambient light.
On the one hand we would like the image intensity to be bright so that we obtain better immunity to noise, but on the other hand we must make sure that the intensity lies below the pixel saturation level. The pixel saturation level varies from one CCD to another, and from one set of data acquisition electronics to another. The length of the cable between the BCAM and the LWDAQ driver also plays a part in determining the saturation level. The LWDAQ can retrieve images across cables up to 100-m long, but a 100-m cable attenuates the image intensity by 17%. If pixel saturation occurs at 200 counts above the background before you introduce a 100-m cable, it will drop to 167 counts above the background afterwards.
You can measure the pixel saturation level of any particular BCAM by flashing a laser at it for one second. The center of the laser image will be saturated, and you will see the spread of pixel charge above and below the center of the image. The intensity of the center of the image is the saturation intensity. This method of measuring the saturation intensity can be fully automated, as it is in the BCAM Saturator tool of our LWDAQ Software.
The BCAM Instrument in our LWDAQ Software will adjust the exposure time for you automatically, and and re-capture the image until it obtains one with an acceptable intensity. In extended acquisition, the software measures the BCAM saturation and background intensities, and adjusts the relative exposure times of multiple sources in the image until they all appear equally bright. The table below shows the exposure times our software arrived at for various camera-source separations.
| Range (cm) | Exposure (ms) |
| 50 | 0.017 |
| 60 | 0.017 |
| 70 | 0.010 |
| 90 | 0.005 |
| 120 | 0.005 |
| 150 | 0.006 |
| 200 | 0.011 |
| 300 | 0.034 |
| 500 | 0.097 |
| 800 | 0.318 |
| 1200 | 0.729 |
| 1500 | 1.041 |
You will notice that the optimal exposure time does not increase as the square of the range between ranges one and five meters. At closer ranges, the light spot spreads out. The light gathered by the camera is distributed over a wider area, so we need a longer exposure time to attain the same intensity.
The brightness of the lasers in our Polar and Azimuthal BCAMs can vary by a factor of five from one laser to the next. This variation comes from the manufacturer's data sheet. Our BCAM laser-driver circuit turns on each laser until its monitor photodiode current is 150 μA. At this current, the laser can emit anything from 1 mW to 5 mW. Our experience has been, however, that the lasers we obtain in one manufacturing lot are similar. We recently measured the output power of ten DL3147 lasers, and they lay within 1.2 mW and 1.4 mW.
Once you have determined the correct exposure time for a particular camera looking at a particular laser, you may still have to change this exposure time in the future. If the image of the laser is small, the exposure time will vary as the center of the image passes across the CCD. When the center lies at the junction between four pixels, the exposure time is at a minimum. When it lies in the center of a pixel, the exposure time is at a maximum. The difference between the two exposure times can be as great as 30%. If you see larger changes in the exposure time, you should capture an ambient-light image and try to see if anything is blocking your view of the laser.
Suppose something blocks some, but not all, of the rays travelling from the laser to our camera aperture. A cable might hang down into the field of view, or a piece of dirt might settle on one side of the lens aperture. In the ideal case of a perfectly focused image, blocking some of the rays does not change the image position. But our BCAM images are in sharp focus only at the focal range.
As you can see in the figure, blocking the aperture when the image is out of focus produces an asymmetric light spot. The images at 50 cm and 15 m are out of focus. The image is in sharp focus at 2.5 m, but when we cover the right half of the aperture we double the angle of diffraction in the left-right direction, and so increase the size of the light spot. Although the focus is sharp, it is not perfect, so that we still see some movement of the image when we block half of the aperture.
| Range (mm) |
x Original (μm) |
y Original (μm) |
t Original (ms) |
x Obscured (μm) |
y Obscured (μm) |
t Obscured (ms) |
x Change (μm) |
y Change (μm) |
| 500 | 1630.65 | 963.85 | 0.025 | 1549.48 | 963.91 | 0.065 | −81.17 | 0.06 |
| 2500 | 2047.91 | 1175.2 | 0.043 | 2052.14 | 1175.12 | 0.160 | 4.23 | −0.08 |
| 15000 | 1241.61 | 1213.2 | 1.20 | 1265.37 | 1212.74 | 28.00 | 23.76 | −0.46 |
As you can see from the table above, the error caused by blocking a portion of the camera aperture changes sign as we go from short to long ranges. It is a range-dependent error, and therefore affects the BCAM's measurement of co-linearity and sagitta. We can, however, detect the presence of dirt on the lens by examining an expanded view of the light spot. We can also detect an obstacle in the light path by taking an ambient-light image of the field of view.
Films of dirt, or finger-prints on the lens, have no effect upon the BCAM other than to decrease its sensitivity to light. A uniform covering of dust on the lens would do the same. Just as a magnifying glass can be remarkably dirty and still function, so can the lens of the BCAM.
If you open up a BCAM to have a look at what is inside, you should check the CCD surface with a magnifying glass to make sure there is no dirt on it before you put the cover back on. Dirt on the CCD appears as black spots in BCAM images of your laboratory, and will interfere with point source images whenever the point source image happens to lie upon one of the dirt fragments.
We check for dirt on the CCD by taking 100-ms ambient light images of a sheet of white paper held 70 cm in front of the camera lens. On the white piece of paper we make a mark with black ink. The black mark gives the BCAM image some contrast with which we can compare spots of dirt on the CCD. We intensify the image display so that any spots of dirt stand out clearly. We blow clean air into the BCAM enclosure to remove dust. We blow on the CCD as well. We clean the CCD with lens paper soaked in glass cleaner. We rub the CCD gently with the lens paper to avoid scratching pieces of the paper off with the sharp edges of the CCD window. We may find that we see gray spots on the CCD when the black mark is out of the BCAM field of view, but that these spots disappear when the black mark returns. Such spots are not opaque, but instead are dots of residual cleaning fluid. You can remove them by cleaning again, but we find that they are not worth removing. When we have no more opaque spots, we seal up the box, put protective tape over the hole in the chassis and the lid, and trust that no more dirt will get in and land on the CCD. Once the BCAM is on its mount, with the mounting screw blocking the hole in the lid, there is little chance of dirt getting into the enclosure. Nevertheless, we recommend that you check for dirt before you mount a BCAM permanently.
Our laser diodes are in 5.6-mm diameter metal can packages. We glue them into the BCAM chassis directly. Our laser driver circuits apply a positive voltage to the laser package, and we rely upon the anodized surface of the chassis to insulate the package from the metal of the chassis. This insulation is reliable when we chamfer and sand the rim of the laser mounting hole before we anodize the chassis.
We made three hundred each of our black and blue azimuthal BCAMs without a chamfer on the laser holes. To fix the problem, we chamfered the holes, stripped the anodizing off, and re-anodized. We still found that some lasers came into contact with the chassis. These BCAMs we mark "Failed Isolation Test". We have been giving these BCAMs out as test pieces. They work fine until you screw them down onto a metal mount. At that point, the screw bites through the anodizing on the cover, and connects the laser cans to the mount. If the mount is grounded, then the laser cans will be grounded, and our laser driver will be unable to turn the lasers on.
By looking at the BCAM images, you should be able to detect and diagnose camera problems.
At ranges shorter than one meter, we see asymmetry in the image caused by reflection off the front and back surfaces of the CCD window. These reflections combine with the original image and give rise to bands of interference . If we remove the glass window on the CCD, the bands disappear. The figure above shows images taken at range 50 cm from various cameras, and the figure below compares images taken from the same CCD with and without its glass window.
Apart from the bands of interference we observe in short-range images, BCAM images should be radially symmetric. If your image is asymmetric in any way at a range greater than one meter, you have a problem. Most likely, there is dirt on the CCD. Take an image of another source, or move the original source within the field of view. If the asymmetry disappears as the image moves, you have dirt on the CCD. If the asymmetry remains, you probably have something blocking the lens aperture close to the lens or dirt on the lens.
Apart from short-range images with a black hole in the middle, all BCAM images should have a bell-shaped intensity profile. If your long-range images have a shroud around them, your BCAM focal range is too short. The lens is too far from the CCD, and your BCAM measurements at long ranges will not be accurate. The image above shows an example of a long-range image with a shroud around it.
We can learn a lot about the performance of a BCAM camera by moving a laser across its field of view with a micrometer stage, and plotting the calculated image position against stage position. If we fit a straight line to this graph, and then plot the residuals from this straight line fit, we obtain graphs like those shown in Figures 13 and 14. The standard deviation of the residuals should be less than half a micron for ranges one meter and up.
If your focal range is shorter than 3 m, you will start to see periodic cycles in your residuals, of amplitude up to 2 μm [10]. With the focal range 3 m, we start to see much larger residuals at ranges less than one meter. The graph below shows the residuals at range 50 cm.
An error of 4 μm on the CCD means a 50-μrad error in source bearing, and therefore a 25-μm error in source position. A BCAM with focal range three meters maintains its 5-μrad resolution for ranges one meter and up. At 50 cm, its resolution is greatly degraded when measured in terms of source bearing. Nevertheless, you may still find the BCAM useful at such short ranges.
We have not been able to break a BCAM by dropping it, and we notice no change in the calibration constants when we drop a BCAM by 30 cm onto a granite table. But the calibration constants of a Black Azimuthal BCAM changed significantly when we dropped it from a height of 1 m onto a concrete floor. The CCD rotated by 2.5 mrad, and the axis direction changed by 400 μrad. We recommend, therefore, that you re-calibrate BCAMs that you drop from more than 30 cm onto a hard surface.
You might be inclined to worry about scratches on the lens, but don't. The glass of the lens is hard, and you would have to deliberately scratch it with a diamond or piece of quartz to make a scratch deep enough to affect the image.
Our chief concern when using BCAMs is that they be fastened properly into their mounts with the correct torque on the mounting screw: finger-tight plus half a turn. If you tighten them more than this, you make a permanent dent in the flat ball space under the chassis, and the BCAM will rotate with respect to its calibrated position. Just by tightening the screw half a turn, you change the axis direction by 20 μrad. Once you have tightened the screw too much in one instance, you will find that the dent you made does not go away, and subsequent correct mounting will not avoid the axis error.
Another concern, as we have mentioned, is dirt on the CCD. You must be careful to keep the two holes in the BCAM taped over at all times, except when you mount it.
The largest voltage available inside the BCAM is 30 V. When we press our tongue against the BCAM power supplies, we feel a sharp sting, but suffer no harm. With our hands, we can feel hardly any sensation, and certainly suffer no harm. If we place the BCAM in water, the power supplies short out to themselves, and disappear.
When secured to its mount, the BCAM will not fall off. The mounting force is many times the weight of the BCAM. You cannot pull a BCAM off its mount with its cable, because the strength of the mounting screw is many times the release force of the connector. We consider the BCAM to be safe for human use under all circumstances.
The BCAM light sources are visible, low-power, and uncollimated. Modern laser safety regulations apply primarily to collimated beams of laser light, but we can apply them to uncollimated light also. A Class I laser is one that cannot deliver the maximum permissible exposure of 4 mJ in 100 seconds. Suppose you tried your best to damage your own eyes with a BCAM. First, you would use the LWDAQ's Diagnostic Instrument to turn on one of the BCAM lasers and leave it on. Second, you would have to pick a BCAM with unusually high power output. Most BCAM lasers produce roughly 1 mW, but a few produce 5 mW. Now you pick up the BCAM and hold it in front of your face. You can't hold it too close, because you can't focus on the source of light, and the chassis touches your eye-lashes. You need to focus on the source of light if you are to concentrate power on your retina and cause it damage. The closest we can hold the BCAM to our eye and get a steady view of the laser, so as to receive the greatest power, is 10 cm. You force your eye to stay open, and stare at the laser.
Kevan Hashemi volunteered to do exactly as described above. But after ten seconds, he could not bear to look at the laser any longer. Doing so was too uncomfortable. For thirty seconds afterwards, he could see a spot in his field of view when he shut his eyes. Also, his eyes were strained from focusing on something so closeby and so bright.
The laser emits <5 mW of red light in a 40° × 20° cone. The power density at a range 10 cm is < 2μW/mm2. While staring at the bright laser, your pupil will contract so that it is no more than 4 mm in diameter. The power received by your eye will be <25 μW. Over a 100-s period, your eye will receive <2.5 mJ, which is below the 4 mJ threshold for biological damage to the eye.
For comparison, consider a 0.2-mW red laser pointer with a 3-mm beam. Such a laser pointer is Class I in the USA, and carries no safety warning label. But it presents 8 μW/mm2 at range 10 cm, sixteen times greater than that of the BCAM lasers. With good collimation, it will present 2 μW/mm2 at a range of 200 cm. The sun delivers of order 200 W/m2 to the earth. With the pupil contracted to 4-mm diameter, the eye receives its maximum permissible exposure after only one second spent staring at the sun. A 60-W incandescent light bulb emits roughly 3 W of visible light. If you stare at a 60-W bulb 35 cm away, you receive 2 μW/mm2, which is the same optical power density you receive from a BCAM laser at range 10 cm.
We conclude that the BCAM lasers fall well within the power limits for Class I lasers, and therefore require no laser power warning labels. We recommend you do not put warning labels upon the BCAM. We believe that doing so is unsafe. If we are to protect people by placing warning labels upon dangerous equipment, we must be sure not to put warning labels equipment that is not dangerous. When people start ignoring the warning labels, they are no longer of any use.
The BCAM is a simple instrument, but there are a number of important rules to follow if we are to obtain its best performance. When we mount a BCAM on its kinematic ball triplet, we must finger-tighten the mounting screw, and then turn the screw only one half-turn further. Before we mount a camera we must make sure that the CCD has no dirt on it by taking images of a white piece of paper with a black mark on it in front of the camera. When the BCAM is in place, we must make sure its field of view is not blocked by taking ambient-light images. We must examine the images we obtain from our light sources and compare them to the example images given in this manual. If a long-range image is asymmetric, for example, or if its intensity profile is not bell-shaped, we can tell that there is a problem with the camera.
If you install and apply your BCAMs correctly, they will provide accurate measurements for many years. The image analysis routine is a simple weighted centroid calculation that is both robust and fast. The geometric principles underlying a BCAM monitoring system are similar to those underlying a theodolite surveying system. Our calibration procedures are robust and need be performed only once during the lifetime of a BCAM. The BCAM camera follows the movement of light sources with 5-μrad (one arc-second) accuracy all across its field of view. It gives us the absolute bearing of a light source with respect to its mounting balls to 50-μrad accuracy. With a system of BCAMs mounted on plates and flexible reference bars, you can measure the geometry of a structure twenty meters across with absolute accuracy better than fifty microns.