2.1

Sensor and Optics

The sensor that we use for the videogrammetric system is a digital 1-mega-pixel space qualified camera (Fig. 2a) which has been developed by Micro-Cameras and Space Exploration SA for ESA’s space missions. It is a compact and light-weight camera which is able to operate in harsh environmental conditions. It is able to work in vacuum and at a temperature down to -120°C without using any canister. With the built in internal heater the sensor is able to work at lower environmental temperatures too.

Fig. 2.

Digital space micro-camera. a) camera with optics and b) micro-LED’s ring flash.

The optics of the micro-camera has a focal length of approximately 12.5 mm and considering the CCD-chip size the field of view is about 78° along the diagonal of the CCD. The aperture of the optics is fixed and is equal to f/10. The Modulation Transfer Function (MTF) of the optics is greater than 50% at 35 lines/mm. The band pass of the optics is approximately between 480 nm and 940 nm.

2.2

Flash

A micro-LED’s ring flash (Fig. 2b) is used with a micro-camera [2]. Micro-LED’s flashes have more reliability and maintainability with respect to tube flashes. In addition, they are able to operate in vacuum and at temperatures down to -180 °C (without canister and thermal protections) therefore no hot spot for the specimen is created by the flash except during the operational time required for the image acquisition. When a LED flash is on, given the duration of the light pulse of 100ms, the transmitting energy is 16J.

2.3

Mechanical Structure

The current videogrammetric system consists of two mechanical structures. Each mechanical structure consists of three parts:

Fig. 3.

Components of the videogrammetric system. a) The movable structure with two micro-cameras and flashes, b) the main structure and c) the support structure.

The videogrammetric network is configured by a vertical translation and rotations of the camera around vertical and horizontal axes. A vertical translation and the rotation around the horizontal axis are actuated by means of stepper motors and can be remotely controlled during the test operation. The rotation of the cameras around vertical axis is set manually before the test and is fixed during the whole test campaign.

The mechanical structure is mainly made of Carbon Fiber Reinforced Plastic (CFRP). It has been designed to be stable with respect to temperature changes, taking also into account dimension variations due to moisture outgassing of the CFRP elements. All the mechanical parts are strictly tolerated to match the alignment and stability requirements imposed for instance by the movable structure which must slide without any jamming. The choice of carbon fiber for the whole main structure system has been made for stability requirements and to minimize mass. Therefore the thermal inertia and the impact over the test specimen will be minimal. The total system weights approximately 13 kg. This makes the system easy to handle by an operator during the installation. For more details see [4].

2.4

Electronics System

The videogrammetry system is controlled by electronic subsystems located inside and outside the thermal/vacuum chamber. The main drivers in the definition of the electrical subsystem are the modularity and fault tolerance. The first is needed to make the system flexible enough to be used with different configurations according to the test. The second is aiming at the reduction (ideally to zero) of the non-recoverable failures that the system might be facing during a test. For more details about electronics system see [4]. The components of the videogrammetric system which are placed inside the vacuum chamber are the harness, mechanical structures, motors, cameras and flashes. The control box, the power supply and the thermal controller are placed outside the vacuum chamber.

3.1

Quality Control of the Targets

Due to a photogrammetric requirement, which is the availability of sufficient number of pixels for the imaged targets, targets with a size of 30 mm are considered. Two types of targets, flat adhesive retro-reflective and spherical targets, will be used for the Herschel videogrammetry. The quality of the targets in terms of accuracy has been analyzed with two algorithms for image processing: 1) center of gravity of the targets and 2) best-fit ellipse of the target edges.

The difference of target center determination with these two methods is 0.14 micron (0.01 pixel) for flat adhesive targets and is 2.1 microns (15 times larger with respect to the flat adhesive targets) for spherical targets. We investigated the reasons that may cause such a large difference between the results of the two methods of target center determination for spherical targets. In the first step we measured the sphericity of the spherical targets with a Coordinate Measurement Machine (CMM), which has an accuracy of 5 microns + 5 ppm. The sphericity was estimated with statistical analysis of the distance of the surface points from best-fit sphere to the surface points. In all cases the maximum distance of the point from sphere was less than 30 microns. The RMS values of the distances are approximately 5 microns. Considering the image scale, this sphericity may cause 0.21 micron (0.017 pixel) error on the imaged target edge localization thus much smaller value than 2.1 microns is expected as the accuracy of the spherical target center. Therefore the sphericity is not the source of the problem.

Another source of error is the inhomogeneity of the target surface reflectance. Due to the inhomogeneous coating, which shows itself particularly with coating of large spherical targets, the reflectance of the surface is not uniform. Fig. 4 shows the reflectivity of flat and spherical targets. The reflectivity of a flat target is uniform therefore the target center with the center of gravity method and best-fit ellipse method are identical with a difference less than 0.005 pixel. The reflectivity of the spherical target is not uniform and as can be seen from Fig. 4 the target center from two different methods has a large shift (0.7 pixel). This shift appears because the center of gravity method is highly dependent on the gray values of the target while best-fit ellipse target edge depends only on the edge information. As a conclusion, both methods have an error but the error from best-fit ellipse method is smaller.

Fig. 4.

Degradation of the target center estimation due to inhomogeneity of target reflectance. a) Flat adhesive retro-reflective target and b) spherical retro-reflective target. The estimated target center from center of gravity method is shown with cross and from the best-fit ellipse target edge is at the intersection of the two lines. The lines are the semi-axes of the fitted ellipses.

3.2

Camera Self-Calibration and Point Positioning

A 3D testfield was established at the ESTEC Test Centre, primarily for the camera calibration. However, it will be used for the calibration and accuracy testing of other metrology instruments like theodolites and laser trackers. The testfield consists of 70 flat adhesive targets, which are homogenously distributed in the area of approximately 4.5 × 2.7 meters. This testfield has been used for the micro-camera calibration.

The camera calibration was performed by self-calibration using Browns’s set of additional parameters [1] and with two more additional parameters specifically for correcting the affinity and shear of the CCD pixels as shown in Eq. (1). Eq. (1) shows the correction terms to the image point observations.

where and with

The photogrammetric network for self-calibration and point positioning consists of 15 stations with 2 images per station with orthogonal rotation around optical axis (kappa rotation). Since at this stage we are not interested in the absolute value of the coordinates, the scale was approximately determined by distance of two targets of the testfield.

The RMS of the image point residuals was in average 0.020 pixel (0.28 micron) for all micro-cameras. The mean standard deviation of the target center coordinates (one-sigma) is 18, 16 and 26 microns along X, Y and Z coordinate axes (X and Y are lateral and Z is depth axis). These values correspond to a global accuracy of 5 ppm. The mentioned global accuracy is calculated based on the estimated standard deviations from least squares optimization method. It is an internal indicator; it is only valid and realistic if there is no (or significantly small) systematic errors present in the measurement.

In the next section we investigate if the standard deviations estimated from bundle adjustment are realistic values or not. Our investigation is based on independent measurements.

3.3

Accuracy Test with Independent Measurement

A flat granite plate with the dimension of 400×300 mm was considered for an accuracy test. 117 targets were stuck on the plate and the target centers were measured with a Coordinate Measurement Machine (CMM) with an accuracy of 7 microns. After best-fit plane the RMSE of the flatness is estimated to be 4 microns.

The flatness of the granite plate was also measured with photogrammetry. After a best-fit plane to the estimated target coordinates from photogrammetry, the RMSE of the flatness was 7.3 microns. This value is approximately 2 times greater than the RMSE of the flatness (4 microns) from CMM. This deviation can be partially explained due to the fact that optical thickness (which is measured with photogrammetry) does not have the same thickness uniformity compared to the mechanical thickness (which is measured with CMM).

The measure of accuracy with flatness is related to the depth axis of the photogrammetric network. The relative accuracy along depth axis is estimated to be 14 ppm. It should be noted that the coordinate determination along lateral axes with photogrammetry is more precise than the depth axis therefore the global accuracy of the system turns out to be 11 ppm.

3.4

Network Configuration

In addition to the sensor accuracy, the configuration of the camera station and object points (network configuration) influence the accuracy of the object point determination. We investigated the accuracy of the object point determination by computer simulations. The following factors were considered with the simulation:

In a network of 96 camera stations with one scale-bar with a length of approximately 1.5 meter and uncertainty of 20 microns (see Fig. 5 for the network configuration), we obtain a mean standard deviation (one-sigma) of 40, 20, 25 microns along X, Y and Z axes. Due to the special design of the videogrammetric system which enables measurement of large and fixed space structures especially in vacuum and under cryo-temperatures, the established network of the camera stations is not able to on-the-job self-calibrate the cameras. In general, there are few solutions to overcome this problem:

Fig. 5.

A Simulated network of 96 stations representing the videogrammetric network of Herschel spacecraft. Two horizontal scale-bars are used.

The first solution requires ad-hoc calibration before the test. The second solution is acceptable if only thermal/vacuum environmental testing is not influenced by the camera thermal perturbation (hot-spots under cryo-temperatures). The third solution is a partial self-calibration of the system under cryo-temperatures, for which a proper strategy is to be considered. The fourth solution is based on the modification of the hardware of the videogrammetric system for a full self-calibration. This approach will be considered in the future. The next section describes this case, which is the preferred one for the Herschel videogrammetric measurement.

3.5

On-the-Job Partial Self-Calibration

As mentioned in the previous section a full self-calibration is not possible with the videogrammetric system due to its specific design. However, a partial on-the-job self-calibration is a solution for the measurement of the Herschel spacecraft.

The negative influence of the additional parameters [6] onto the object point coordinates has been analyzed. The summary of the calculation is shown in Table 1. It shows how the standard deviations of the object point coordinates and the differences from the true values are degraded because of the negative influence of additional parameters. It shows that S_x (affinity parameter) has the highest negative influence on the object point coordinates. Fixing S_x improves the accuracy by a factor 1.4. The other parameter with highest correlation to the object point coordinates is a (shear parameter). After fixing this parameter the accuracy of the object points is improved by a factor 2 with respect to a full self-calibration. Better accuracies can be achieved by fixing more additional parameters. We only consider the case with fixed (S_x, a) because these two parameters will remain constant at cryo-temperatures [7] and it is feasible to fix them to the a priori values, which is calculated at ambient temperature.

Table 1.

The negative influence of Additional Parameters (APs) on the object point coordinates. Standard deviations are one-sigma. The units of the standard deviation and RMSE are microns.

An additional investigation shows that by fixing (S_x, a) the negative influence of the other additional parameters would remain constant if only the network of measurements (including the point coordinates) had a differential changes (<15 cm). Considering this fact, these errors can be eliminated by subtraction and the point coordinate accuracy can be improved by a factor 2. The mentioned numbers in Table 1 are from computer simulations and may differ from reality. Therefore real tests have been performed in order to validate the result of partial self-calibration and accuracy improvements. The results are presented in next sections.

3.6

Qualification of the System

Each component of the videogrammetric system has been separately validated for operation in ambient and cryogenic conditions. The overall operation of the system in cryo-temperatures has been qualified during the pre-test of the Large Space Simulator (LSS) for GOCE spacecraft.

The validation of the videogrammetric system accuracy has been done for each micro-camera separately after an investigation of their potential accuracy. The accuracy of the overall videogrammetric system was estimated through computer simulation. However, it was obviously necessary to confirm this estimate in a real situations. A setup as shown in Fig. 6 was prepared and it represents approximately the Herschel spacecraft target configuration with 12 spherical and 20 flat adhesive targets. Two independent measurement methods have been used:

Fig. 6.

A dummy object (a) and the videogrammetric system (b) in the Hydra clean room at ESTEC Test Centre. It shows the location of the spherical (top at the rim) and flat adhesive targets (on the body and lower than the spherical targets) simulating the configuration of the Herschel spacecraft (copyright ESA-ESTEC).

In total five different cases for accuracy tests have been compared:

The accuracy of the probed points on the surface of the spherical targets was estimated with a laser tracker simulation software, Spatial Analyzer, which is 38, 45 and 43 microns along X, Y and Z axes. By error propagation through best-fit sphere the accuracy of the spherical target center measurement was estimated 18, 20 and 22 microns along X, Y and Z axes. The RMS of the difference of the spherical target center coordinates from videogrammetry and laser tracker is 100, 110 and 73 microns along the X, Y and Z coordinate axes. This relatively large RMS value is due to the poor quality of the spherical targets that cannot be measured accurately with photogrammetry.

The accuracy of the flat and spherical target center measurements with theodolite is 70, 60 and 90 microns along X, Y and Z axes. The RMS of the difference of the target center coordinates from photogrammetry and theodolite measurement is 80, 100 and 100 microns along the X, Y and Z coordinate axes. If we only consider flat adhesive targets the RMS of the coordinate difference becomes 70, 40, 70 microns. The RMS of the point coordinate differences from a case with a partial self-calibration and a case with fixed additional parameters is equal to 108, 46 and 82 microns, which are approximately equal to the results of simulated network. A part of this difference can be explained by the difference between the simulated network configuration and the real network configuration for validation. After fixing (S_x, a) the pattern of the negative influence of additional parameters does not change significantly by a small change of the network configuration. Therefore it is able to improve the accuracy by a subtraction of the point coordinates of two sets of measurements down to 51, 55 and 46 microns. Therefore the accuracy obtained from videogrammetry fulfills the requirements of the Herschel spacecraft measurements (50 microns one-sigma).