LEICA DMC III CALIBRATION AND GEOMETRIC SENSOR ACCURACY

As an evolution of the successful DMC II digital camera series, Leica Geosystems has introduced the Leica DMC III digital aerial camera using, for the first time in the industry, a large-format CMOS sensor as a panchromatic high-resolution camera head. This paper describes the Leica DMC III calibration and its quality assurance and quality control (QA/QC) procedures. It will explain how calibration was implemented within the production process for the Leica DMC III camera. Based on many years of experience with the DMC and DMC II camera series, it is know that the sensor flatness has a huge influence on the final achievable results. The Leica DMC III panchromatic CMOS sensor with its 100.3mm x 56.9mm size shows remaining errors in a range of 0.1 to 0.2μm for the root mean square and shows maximum values not higher that 1.0μm. The Leica DMC III is calibrated based on a 5cm Ground Sample Distance (GSD) grid pattern flight and evaluated with three different flying heights at 5cm, 8cm and 11cm GSD. The geometric QA/QC has been performed using the calibration field area, as well as using an independent test field. The geometric performance and accuracy is unique and gives ground accuracies far better than the flown GSD.


INTRODUCTION
The first single CCD array for the large format digital frame camera, Z/I DMC II, was introduced to the market in 2010.With this introduction, the geometric performance increased by an order of magnitude of the initial performance.With the DMC II development, the geometric calibration moved from an Australis Model base to a Grid-based calibration.A two-step calibration had been performed using a collimator measurement as an initial calibration and enhanced the geometric accuracy by introducing a distortion grid correction.The Z/I DMC II geometric calibration takes place at Carl Zeiss Jena on a certified test stand.More than 800 "light targets", projected on 28 lines that are distributed diagonally on the focal plane, are automatically measured by finding their light centers with a precision of less than 1/10 of a pixel.The light targets are projected from "infinity" using a collimator (Figure 1).The grid-based calibration procedure can model aspheric lenses and much more accurately models local distortions.The Leica DMC III uses the same lens system that was employed for the Z/I DMC II 140 and 230 models.It is equipped with a very large single CMOS sensor with a physical size of 26112 x 15000 pixels, with a pixel size of 3.9μm.The Leica DMC III cannot be calibrated using the calibration procedure established for the Z/I DMC II series (using the standard calibration stand at the Zeiss factory), due to calibration stand's limited positioning accuracy of the camera in front of the collimator.
For the pixel size of 3.9μm, the targeted 1/10-of-a-pixelmeasuring performance cannot be achieved.As a solution, a so-called "SYNTHETIC" geometric calibration was established, which is based on a simulated mathematical lens distortion calculation based on the detailed optical design data of the lens.It is equivalent to the DMC II collimator calibration procedure, projecting 800 "light targets" on 28 lines that are distributed diagonally on the focal plane (Figure 1).The large sensor size across flight direction maximizes the utilization of the optical circle.This in turn increases the amount of distortion on the outer edges of the image frame.The challenge of the new calibration concept was to achieve the same or better geometric performance that was obtained with the DMC II camera models.

FLIGHT CALIBRATION BLOCK
To perform a DMC III geometric in-field calibration, a welldefined calibration field is required (Figure 2).Some general requirements for the calibration field must first be fulfilled.
A square calibration field over the city of Aalen was used, covering this field with a grid pattern of 5 flight lines in the North-South direction and covering the same area with 5 flight lines in the East-West direction.The Ground Sample Distance (GSD) for the calibration purpose is 5cm, and the whole calibration field is well distributed with visible control points.
To ensure the calibration procedure, the 2.5x2.5km²calibration field is covered by 90-95 ground control points (GCPs) with a high horizontal and vertical accuracy.The standard deviation of the available GCPs is 2-3cm in the horizontal direction and 3-4cm in the vertical direction.If some GCPs are covered by objects, there are always many alternative points available.The flight lines are planned with a 75% forward and 75% side overlap to achieve a huge number of multi-ray object points.
For the calibration procedure an almost flat terrain over an urban area is preferred to achieve a constant GSD over the block.For final geometric calibration of the multispectral camera sensors, sharp contours are needed within the calibration field.In addition, the area should not include a large number of large trees.Since trees are objects that move with wind, they have a negative impact to the color registration during the calibration procedure.However this paper covers the geometric calibration procedure for the PAN sensor only, since this is relevant for the Leica DMC III geometric performance only.The calibration procedure is based on highly accurate GNSS/IMU data, therefore it is recommended to have a GNSS ground station within the calibration field to achieve the highest DGNSS accuracy.To achieve the best possible GNSS/IMU accuracies, a couple of requirements for the practical flight performance must to be addressed.About 3-5 minutes before the first exposure is taken, a so-called in-air alignment (figure-8 or S-curve) (Figure 3) needs to be performed to achieve highest IMU data quality.The same procedure needs to be performed 3-5 minutes after the last exposure was taken.The flight lines need to be flown in an alternating procedure (Figure 3) to eliminate systematic influences such as a smaller datum shift, small errors in aircraft GNSS antenna offsets, and to be able to compute the sensor-specific principle point of Auto Collimation (PPAC).

CALIBRATION PROCEDURE
During the geometric calibration for the Leica DMC III camera, the knowledge of the sensor flatness, its tilting against the nadir position with respect to the optical axis and the lens distortion needs to be determined and represents the geometric calibration procedure.The interior flatness of the sensor itself is determined during the production at the factory (Figure 4) and is excluded when exceeding ±30μm.The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-3/W4, 2016 The geometric calibration for the Leica DMC III is divided into 4 calibration steps.
GOLD  PLATINUM It is an iterative process in which the last step represents the final QC/QA step and provides the final camera accuracy, which serves for validating the targeted sensor accuracy and the calibrated focal length and principle point of auto collimation.
For the calibration steps 1-3 a fully-triangulated Intergraph ISAT project was used that follows the grid calibration guidelines.A grid calibration is used because, in contrast to an Australis model, it is able to represent aspheric lenses, and it can model local distortions more precisely.For steps 1-3, the image standard deviation is relaxed to 8μm (Table 1), and fullcalibration-frame images are used (Figure 5).The fullcalibration-frame images are used to get a more precise knowledge of the image distortions at the borders and edge parts of the sensor.The result is a more precisely computed distortion grid for the final image size.For the final image a reduced image size of 25728 x 14592 pixels is used.The mechanical FMC makes this size reduction necessary.2) from one calibration iteration step to the next, since the remaining distortion becomes smaller and smaller.

Calibration Step Tie/Pass
Table 2. a posteriori clean-up criteria for AT calibration steps

LEICA DMC III CAMERA GEOMETRY
The camera geometry is expressed by the image geometry that means the systematic image errors describing the difference between the real image geometry and the mathematical model of the perspective geometry (Jacobsen, Neumann 2012).
Based on the calibration procedure, the remaining image distortions are getting reduced significantly from one calibration iteration step to the next (Figure 9 and Table 4).The final QA/QC step is performed to estimate the final remaining image distortion.A grid distortion plot, as well as a separated transversal and radial distortion plot, is produced and published within the camera calibration report.Furthermore, a bundle block adjustment analysis is performed, based on a typical photogrammetric block.All calibrated camera systems are within the specification and differ only from system to system (Table 5).The Mean RMS in X and Y direction must not exceed 0.2μm while the Max RMS in X and Y direction must not exceed 0.8μm.The differences from system to system are caused by differences atmospheric and image point accuracy differences, as well as the physical location of the sensor within the focal plane and its resulting larger edge distortion.The averages of the root mean squares of the residuals shown in Table 5 do not exceed 0.2μm and shows the largest values below or equal to 0.7μm.The final PLATINUM calibration shows no obvious systematic trend; almost all systematic effects that were clearly visible within the iteration steps 1 (SYNTHETIC  BRONZE) and 2 (BRONZE  SILVER) are elimiated.Some systems show slight radial distortion effects at the image corners and Y-direction edges due to fact that the sensor is coming very close to the brink of the optics.

Block Layouts
The geometric performance of the Leica DMC III was checked with different evaluations and test flights.The main evaluation datasets are taken with a 5cm GSD over the city of Aalen and with a 5cm GSD close to the city of Nördlingen.A second evaluation flight was performed with an 8cm GSD over the city of Aalen and with an 11cm GSD over the Nördlingen area.The 11cm evaluation dataset was taken in a double cross pattern flight instead of a block layout flight.This was mainly used to check the performance of the calibrated nominal focal length.Two more test datasets were taken over a customer airfield with a 7cm and 14cm GSD.The performance of the Leica DMC III was proven using a block layout with and without cross flight lines.The red surrounded ground points were used as control points, while non-surrounded points were used as check points (Figure 10).The block adjustments for all evaluation and test datasets show similar results and trends.The average Root Mean Square in horizontal direction of the check points is at 0.41 of a pixel, The average Root Mean Square in vertical direction for the check points is at 0.65 of a pixel.The results are depending on the block configuration, the overlap and the number of check and control points used.In one single evaluation case the maximum horizontal Root Mean Square was 0.66 of a pixel and the maximum vertical Root Mean Square was 0.92 of a pixel.The target is a horizontal RMS of 0.50 of a pixel in horizontal and 0.70 of a pixel in vertical.

INFLUENCES OF PERIPHERAL SYSTEMS
The in-flight calibration accuracy of a Leica DMC III is not a sensor-and-calibration-procedure-specific task; it is rather influenced by peripheral systems as well.It is without question that all peripheral systems must perform as accurately and precisely as possible to achieve a highly-qualified geometric camera calibration.Two peripheral systems that influence the sensor geometry most significantly are the mechanical Forward Motion Control (FMC) and the stabilization of the sensor during the image release procedure.

Mechanical FMC and its geometric influence
With the Leica DMC III Pan (CMOS Sensor) a new technique for the forward motion compensation (FMC) is introduced in the DMC family.While for CCD sensor the well-known Time Delayed Integration (TDI) is used.For CMOS this approach is not possible due to different read out strategies.The CMOS sensor must be moved mechanically to correct for the forward motion influence.
For this the Leica DMC III Pan camera head is equipped with a brushless drive; it is a DC-Motor with a gear and an excentric, that moves the sensor carriage.The Figure 15 is showing the movement and acceleration of the sensor in respect to exposure start.It is shown that the sensor is accelerated shortly before exposure start and moves with a constant speed during shutter opening.Following the sensor movement it will slow down and the sensor moves back to its starting position for the next exposure.
The measurement is done with a very accurate device achieving an accuracy of 50 nm.For the geometric accuracy it is important that the interior orientation (sensor position) will not change over all exposures.Also the movement of the sensor during exposure should coincide with the real movement over the ground.
To simplify we assume that during the short exposure time period there is no change in flying speed and height over ground, so that the sensor should move linear.Figure 16 is showing the absolute difference from the linearity of one exposure, while Figure 17 and Figure 18 displays the standard deviation from the linearity of one flight project.The performance above shows that FMC does not have a significant disadvantages compared to TDI regarding image geometry, the opposite is true.Due the possibility of sub-pixel correction a higher performance can be achieved.TDI is able to correct for full pixels only while the FMC has a theoretical standard deviation of 1μm which is ¼ of a pixel.Practical experiences are showing a much better performances, with a standard deviation of ⅛ of a pixel only.

Sensor stabilization and its geometric influence
Any sensor movement during the exposure release will cause a radiometric image degradation, in the form of blurring..Those will be greatest at the image corners.For geometric calibration purposes, the radiometric effects are not the most important issues, rather the pixel displacement must be highlighted.This results in a geometric pixel displacement, which influences the final computed sensor distortion model.The smaller pixel size, the high performant FMC and the high performant camera stabilization provided by the gyro-stabilised sensor mount makes the contribution to perform flights with a very small GSD (down to 3cm).Practical experiences showed very stable and sharp image results even for this challenging ground resolution.This overtakes the operating conditions of most other digital aerial cameras on the market, with respect to geometric accuracy and blurring free image data.

Figure 1 .
Figure 1.Light Target Pattern by Collimator SYNTHETIC Light Target Simulation

Figure 2 .
Figure 2. Leica DMC III calibration flight footprints overlap with Ground Control Point distribution

Figure 5 .
Figure 5. DMC III nominal and absolute image frame size

Figure 6 .
Figure 6.All image points overlaid to one image

Figure 7 .Figure 8 .
Figure 7. Image point distribution over the triangulation block On each calibration step, a post-correction grid file is generated.The number of columns and rows in the grid file accumulates image residuals in the camera frame.It is recommended for DMC III cameras to use roughly 1024x1024 pixel collection cells per quadrant.Two by Two quadrants are used that results in a total cell number of [15000 26112]/1024 = [14.648425.5000], which rounds up to 2*[15 26] = [30 52] total number of cells.For each calibration iteration, a post-calibration tool produces the IPMM file, based on the generated post-correction grid file for the next calibration iteration step (Table3).It always refined the previous calibration for its remaining non-linear systematic distortion trend in the focal plane that could not be absorbed by the optimal selection of the focal length and principle point of Auto Collimation, which is only a scale/bias type of correction.The final calibration step, GOLD  PLATINUM, is not another step of grid refinement.It is used to scale the GOLD calibration grid calibration from its calibrated to its nominal focal length and principle point of auto collimation.

Figure 9 .
Figure 9. Distortion plots overview of iteration steps

Figure 10 .
Figure 10.Flight pattern with control and check point configurations for evaluations and test datasets

Figure 11 .
Figure 11.RMS of check points for different blocks and configurations as described

Figure 13 .Figure 14 .
Figure 13.RMS of control points for different blocks and configurations as described

Figure 15 .
Figure 15.FMC Movement in respect to shutter opening and exposure start

Figure 16 .Figure 19 .
Figure 16.Difference to linear movement Figure 20 shows a unifilar drawing of the 3-dimensional influences of image motions during exposure release.The following equations (1) -(5) were used to calculate and analyse the number of pixel displacements during a calibration flight.The corner point of a Leica DMC III image was taken (the largest pixel displacement effects are visible at this extreme point).

Table 3 .
Evolution of the IPMM grid calibration file

Table 4 .
Remaining camera distortion values between different iteration steps

Table 5 .
Remaining camera distortion values between different camera systems