EVALUATION OF RESOLVING POWER AND MTF OF DMC

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1 EVALUATION OF RESOLVING POWER AND MTF OF DMC E. Honkavaara 1, J. Jaakkola 1, L. Markelin 1, S. Becker 2 1 Finnish Geodetic Institute, Masala, Finland (eija.honkavaara, juha.jaakkola, 2 University o Stuttgart, Institute or Photogrammetry, Stuttgart, Germany Commission I, WG I/4 KEY WORDS: Aerial Digital Camera, Calibration ield, CCD, Photogrammetry, Quality, Resolution ABSTRACT: The present article reports the results o an extensive empirical evaluation o spatial resolution o a digital large ormat Intergraph DMC sensor. The parameters o the study were light direction, ground sample distance (GSD) and the distance rom the image center. The key inding o the study was that the resolution o the DMC panchromatic large-ormat image was clearly dependent on the distance rom the image center. One reason or this behavior is that the DMC large-ormat image is composed o our oblique images; the resolution o the oblique images is reduced towards the image border due to the scale reduction and projective distortion. From the image pixel size o 12 µm o DMC, a nominal resolving power value (RP) 84 lines/mm can be derived. Maximal resolution reduction actors in the image corners, caused by the image tilt, were 1.6 in the cross-light direction and 1.4 in the light direction. The distance rom the image center did not appear to aect the resolution o the low-resolution multi-spectral images looking towards nadir. The observed MTFs indicated attractive behavior. The AWAR values o the panchromatic images were between 61 and 71 lines/mm, which is times the nominal RP-value. Other important indings were the eects o GSD and light direction on the resolution; these properties evidently characterize the behavior o the entire photogrammetric system tested. The image restoration by a linear restoring inite impulse response ilter provided a constant resolution improvement actor o INTRODUCTION A key quality component o the photogrammetric sensors is spatial resolution. In the case o digital sensors, the pixel size limits the spatial resolution attainable. However, in practice the nominal resolution is seldom achieved due to blur and noise caused by many actors. Key actors aecting the image resolution are the camera (e.g. optic, CCD, orward motion compensation), the system (e.g. mount, camera port glass), the light actors (e.g. light altitude, light velocity, aperture, exposure), atmosphere and object actors (e.g. sun height, air turbulence, visibility) and data post processing (Hakkarainen, 1986; Read & Graham, 22). Due to the large number o actors involved, it is crucial to test the perormance o the entire photogrammetric production line empirically. In the case o the DMC, undamental actors aecting sensor resolution are the properties o the CCD, the optics, the TDI orward motion compensation, the resampling process where the large-ormat panchromatic images are generated rom oblique medium-ormat images, and the pansharpening process o the multi-spectral images. (Hinz et al., 2; Tang et al., 2) The objective o this study is to investigate the resolution o the Intergraph DMC digital large-ormat photogrammetric sensor. The results are o importance or the urther development o test ield based calibration methods, or the understanding o the perormance o the digital sensors, or the selection o appropriate GSDs or practical mapping tasks, and or evaluating the perormance o the photogrammetric system. The test set up is described in Section 2. The results are given in Section 3 and the most important indings are summarized in Section DMC test lights 2. EXPERIMENTAL STUDY DMC test lights were perormed at the permanent Sjökulla test ield o the Finnish Geodetic Institute (FGI) (Kuittinen et al., 1994; Kuittinen et al., 1996; Ahokas et al., 2; Honkavaara et al., 26) on September 1-2, 25. The test lights were perormed in co-operation with the National Land Survey o Finland (NLS). The survey aircrat was the OH-ACN belonging to the NLS (Rockwell Turbo Commander 69A turbo twinpropeller aircrat with a pressurized cabin and two camera holes). The weather conditions during the campaign were excellent. The DMC was mounted on a T-AS gyro-stabilized suspension mount. Images with 5 cm and 8 cm ground sample distance (GSD) were studied (,, ; Table 1). Two similar blocks with 8 cm GSD were collected in consecutive days. Resolution targets were located in dierent parts o the image (Figure 1). The raw images collected were processed using DMC Post processing sotware (Version 4.5). Only linear tonal transormations were applied in the image processing; 16 bit/pixel images were used. Analog reerence images were collected simultaneously by a RC2 belonging to the NLS (the exposures were not synchronized). Panchromatic and color ilms, and a 15 mm wide-angle optic were used. The camera mount was a PAV 11A-E (not gyro-stabilized) and FMC was applied. The ilms were scanned by a Leica Geosystems DSW 6 scanner with a 15 µm pixel size and 8 bit/pixel pixel depth. 2.2 Methods A permanent dense bar target and a portable Siemens star were used to evaluate the spatial resolution. The dense bar target is a 4-bar square-wave target (Figure 2) made o gravel. The target is aligned in two perpendicular directions. The widths o the

2 Table 1. Test blocks (n/a=not available due to missing metadata) Block Date Time 1:25-11:14 11:24-11:53 9:56-1:9 GSD (cm) Optic (mm) Flying speed (m/s) n/a Exposure (ms) 6.3* 6.* n/a -stop n/a Flying height (m) Scale 1:4167 1:6667 1: 6667 Swath width (m) Overlaps (%) p=q=6 p=8, q=6 p=8, q=6 *) Automatic exposure, average c Direction o light Figure 2. Dense resolution bar target. Direction o resolution measurement: c: cross-light, : light. Figure 3. Portable Siemens star on ground and with 4 cm, 8 cm, 25 cm and 5 cm GSD. Direction o resolution evaluation c: cross light, : light; lying direction is rom let to right or right to let. c Figure 1. Distribution o resolution targets on images. bars varies rom 3 cm to 12 cm, and the bar width increment is 6 2 ( 12%). In this study, the low contrast target (contrast 1:2) was used. The portable Siemens star (a semicircle) has 1º sectors and a 6.8 m radius; the maximum sector width is 1 m (Figure 3). Contrast is 1:5-1:11, depending on the wavelength. The resolution evaluation was based on the resolving power (RP) and the modulation transer unction (MTF). The resolution was measured in the light and in the cross-light directions. In order not to reduce the quality o the analysis by subjective interpretation, highly automated methods have been implemented in the FGI s own RESOL sotware or the measurement o bar targets and Siemens star. RESOL version 3..4 was used in the study Measurement o bar targets. In the irst RESOL version, the RP was calculated rom microdensitometer proiles (Kuittinen et al., 1996; Ahokas et al., 2) but nowadays 8 or 16 bit/pixel digital images are used. Several types o bar targets with dierent combinations o line width, space and number can be measured. Ater loading the image, the position o the center proile o the test target is marked. Because the target is typically slightly rotated, the intensity values o the proile points are calculated using bilinear interpolation. The required number o parallel proiles is then generated at a distance o one pixel rom the neighboring proile. The program locates iteratively the maximum and minimum points on each proile using also geometric constraints set by the dimensions o the target on the ground. A certain requency on a proile is accepted as recognized i: 1. All minimum and maximum points o the requency are ound to be in correct geometry, and 2. The dierence between means o maximum and minimum values exceeds the combined standard deviation o maximum and minimum values multiplied by a parameter value. The parameter can be deined empirically by comparing results with visually deined values. A commonly used value is 2. A requency is regarded as recognized i it is accepted on more than 5% o all proiles. Finally, the MTF curves are calculated rom the same proiles using equations 1-3, i necessary. The RP, true ground sample distance (TGSD; width o the smallest detectable line on ground), and area weighted average resolution (AWAR; Ahokas et al. 2) are calculated on the basis o the highest recognized requency MTF determination rom Siemens star. The method in the RESOL sotware is based on the Stuttgart method described by Becker et al. (25, 26). First o all, the contrast transer unction (CTF) is obtained as the quotient o the image and the object modulations (M): I max I min M = (1) I + I max M image CTF = (2) M object The object modulation is obtained rom the image using minimum and maximum values rom a suiciently large area o the background and object materials. As the targets are square wave targets, the CTF is transormed to MTF by series conversion (Coltman 1954). Typically the observed MTF is evaluated. For the urther analyses a Gaussian shape unction is itted to the obtained MTF data (Becker et al., 25; 26): 2 2 σ MTF 2π K MTF e, (3) where K is the requency in cycles/pixel. min 2

3 Ater measuring an approximate center point o the Siemens star, the RESOL sotware perorms the ollowing steps to determine the MTF: 1. Deines the radius o the star and creates circular intensity proiles. 2. Locates the edge points between white and black sectors. 3. Calculates straight lines or edges and the center point as the intersection o these lines. 4. Collects intensity data rom bisections o the sectors. 5. Calculates MTF rom selected sectors (vertical and horizontal sector pairs or quarter circle). 6. Fits the Gaussian shape unction to the observed MTF. Parameters are σ PSF (or σ MTF ) and an additional scaling actor to compensate or the missing -requency value. p s 1 k α β 2 α h x = h cos β s cos( α + β ) k p k α2 = arctan( ); β = arctan( ); s s 2 1 sin( β α2) sin(9 α α ) 2 1 = cos β In this study, the MTF was calculated or sector pairs in light and cross-light directions, and or all directions using a quarter o the Siemens star (the sector pairs aligned in the light direction, perpendicular to light direction, and between these). From the MTF, various measures o resolution can be derived. In this study, the standard deviation o the Gaussian shape point-spread unction (σ PSF ; Becker et al., 25; 26) and 1% MTF (an estimate o the RP-value) were used Image restoration. Resolution evaluation and restoration o the high-resolution panchromatic images was perormed at the Institute o Photogrammetry at Stuttgart. The methods are described in detail by Becker et al. (25, 26). 3. RESULTS Figure 4. Geometry o a tilted camera. α=tilt angle, h=lying height, p=pixel size in image, =ocal length, k=image side length/2, x=size o image pixel on image border on ground. y x x 3.1 Theoretical expectations The large-ormat panchromatic image o size 768 x pixels (92.16 mm x mm) is composed o our mediumormat images o size 496 x 7168 pixels ( mm x mm), which are collected by our divergent cameras. The approximate tilt angles o the sub images are 1 in light direction (x direction) and 2 in cross-light direction (y direction). The pixel size is 12 µm and the ocal length is 12 mm. Four lowresolution multi-spectral channels having a pixel size 4 times larger than the panchromatic images are collected using our cameras o size 3k x 2k pixels looking towards nadir. Highresolution multi-spectral images are provided by pansharpening. (Hinz et al. 2; Tang et al. 2). The 12 µm pixel size gives a nominal RP value o 84 lines/mm. In reality the resolution is not constant in the area o the large ormat virtual image, which is constructed o oblique component images. The image scale decreases with the increasing distance rom the image center as shown in Figure 4. Assuming tilt along one axis only, the size o a pixel in the image border on the ground (x) is obtained rom the geometrical relationships (Figure 4). The resolution reduction actor in the border o the component image is 1.5 in the y direction and 1.1 in the x direction. The reduction is larger in the y direction because o the larger tilt angle and the larger image width. In reality, the sensor is tilted along both the x and y axis, so the relationship is more complicated. The scale reduction actors in the area o one component image in x and y directions are shown in Figure 5. The igure was provided by projecting a regular grid rom object to image and comparing the distances o the points to nominal distances calculated by the nominal scale. The actor between the nominal and true scales is Figure 5. Formation o the large ormat panchromatic image (let). Resolution reduction actors in x (center) and y-directions (right) or the top-let component image. between.9 and 1.6 in the cross-light direction and between.9 and 1.4 in the light direction. These reduction actors and the 12 µm pixel size lead to a resolution o between 53 and 84 lines/mm in the cross-light direction and between 6 and 84 lines/mm in the light direction. 3.2 MTF Figure 6 gives the observed MTFs in line pairs per pixel () o 13 images o block in all, lying, and crosslight directions. The observed MTFs are given in order not to smooth details; data points are presented in Figure 8. Dierences appeared in the MTFs o various images and the behavior was similar with 8 cm GSD. These dierences were caused mainly by resolution dierences. Some instability appeared especially on the MTFs o sector pairs; the instabilities were mainly caused by the topography o the object. Despite this, the MTFs o DMC appeared to show attractive behavior. The downall o the MTF at a requency o.4 indicated that the system resolution was lower than the nominal resolution (.5 ). Figure 7 shows the eect o GSD on the resolution (average all, light and cross-light direction MTFs). The MTFs o two blocks with 8 cm GSD were practically the same. The MTF o the 5 cm GSD block was slightly worse than that o the 8 cm GSD blocks.

4 1.2 All directions 1.2 Fight direction 1.2 Cross-light direction Figure 6. Observed MTFs or 13 images o block. Let to right: all, lying, and cross-light direction. 1.2 All directions 1.2 Flight direction 1.2 Cross-light direction Figure 7. Average MTFs. Evaluation the eect o GSD. Let to right: all, lying, and cross-light direction All c All c All c Figure 8. Average MTFs. Evaluation o the eect o lying direction. Let to right:,, and. Figure 8 shows the eect o light direction on the resolution (average MTFs). In each case the MTF was the best in the cross-light direction and the worst in the light direction. In these plots the data points that created the MTFs are also given. The object modulation was obtained rom the Siemens star itsel, which is the correct approach only i the GSD is small enough. With too large GSDs, the MTFs become optimistically biased. With an 8 cm GSD, the widest sectors were 12.5 pixels and with a 5 cm GSD the widest sectors were 2 pixels, which should be suicient. The scale parameter estimated in the MTF calculation should also compensate or this problem. 3.3 Resolving power The RP values were derived both rom the bar targets and rom the Siemens star (1% MTF). The RP values in the light and cross-light directions are shown or each block as a unction o the distance rom the image center in Figure 9. Approximate theoretical resolutions are presented or the light and crosslight directions (linear unctions between minimum and maximum expected RP values; Section 3.1). It appeared that the distance rom the image center radically aected the resolution. Central reasons or this behavior are the ormation o the large ormat image rom oblique component images and possibly also the decrease o the lens resolution towards the image border. Extensive empirical tests with analog systems have shown similar dependence on the radial distance, but at least partly or dierent reasons (e.g. Hakkarainen 1986). Comparison to simultaneous analog images indicated quite similar RP values, but the general MTF perormance o the DMC was more attractive. AWAR values are given in Table 2. For instance, the bar targets gave AWAR values o between 61 and 71 lines/mm. AWAR values in the light direction were lines/mm and in the cross-light direction lines/mm. The ollowing average reduction actors rom the nominal resolution could be derived: GSD 5 cm: light: 1.5, cross-light: 1.3 GSD 8 cm: light: 1.3, cross-light: 1.2 On average, the RP values given by the bar targets were 1% higher than the 1% MTF values. The dierences between individual images were airly large, but the average values and general trends were consistent. With 8 cm GSD, the limited size o the bar target caused diiculties or automatic measurement (widest lines were 12 cm).

5 Siemens, : y = x R2 =.521 c: y = x R2 =.1145 c Theor_ Theor_c Linear (c) Linear () Siemens, : y = x R2 =.6442 c: y = x R2 =.728 c Theor_ Theor_c Linear (c) Linear () Siemens, : y = -.413x R2 =.5859 c: y = x R2 =.7763 c Theor_ Theor_c Linear () Linear (c) Bar target, : y = x R2 =.7981 c: y = x R2 =.3424 c Theor_ Theor_c Linear (c) Linear () Bar target, c: y = -.76x R2 =.2 : y = -.513x R2 =.5273 c Theor_ Theor_c Linear (c) Linear () Bar target, c Theor_ Theor_c Linear (c) Linear () 4 : y = -.37x R 2 = c: y = -.397x R2 = Figure 9. Resolving power measurements as the unction o the distance rom the image center. Top: 1%MTF rom Siemens star, Down: RP rom dense bar target. Blocks rom let to right:,,. (: resolution in light direction, c: resolution in cross-light direction) 3.4 Resolution o non-pansharpened color images The MTFs o the non-pansharpened color images were evaluated using the Siemens star. Data rom the block was used; the GSD was thus 2 cm. The 1% MTF values are given as a unction o the location in Figure 1. The location did not appear to aect the resolution o the color images. The color images had distinctly higher RP-values than the panchromatic images. The green and blue bands had the best resolution (approx. 85 lines/mm) while the red channel had the worst resolution (approx. 8 lines/mm). Resolution o the color images was slightly better in the cross-light direction than in the light direction. It is possible that the values were optimistically biased because the.2 m GSD is relatively large or the Siemens star used in this study (Section 3.2). 3.5 Image restoration The images were restored using the methods described by Becker et al. (25, 26). Eects o the image restoration on the σ PSF are shown in Figure 11. The restoration resulted in a constant resolution improvement, which was similar or each test block. On average, the σ PSF values o the restored images were better than those o the original images by a actor o 1.4. Table 2. Average resolution (direction : light, c: cross-light). AWAR (lines/mm) Siemens Bar AWAR_ (lines/mm) Siemens Bar AWAR_c (lines/mm) Siemens Bar Average σ PSF All (pixel) Flight Cross-light SUMMARY AND CONCLUSIONS The resolution o an Intergraph DMC large-ormat photogrammetric camera was studied using extensive empirical test light data. The parameters o the study were the light direction, the lying height and the distance rom the image center. The analysis showed that the resolution o the large-ormat panchromatic images was dependent on the distance rom the image center. One important reason or this behavior is that the component images are oblique, which causes smaller scale and reduces the resolution towards the image border. Also the reduction o the lens resolution towards the image borders can contribute to the phenomenon. Details o the lens MTFs would make more detailed analysis o the eect o various actors possible. The resolution o the vertical non-pansharpened color images was not aected by distance rom the image center. Evaluation o the eect o the lying direction showed that the resolution was worse in the light direction than in the crosslight direction. One possible reason or this could be a slight insuiciency o the orward motion compensation. The resolution appeared to improve with increasing GSD. The probable reason or this is that the image motion is relatively smaller when the GSD is larger. It is possible that these phenomena are related to the entire imaging system. The test lights were perormed using a low lying altitude with relatively high lying speed; dierent conditions might lead to dierent results. In the uture, ield calibration will be used increasingly to test and validate photogrammetric systems. It is important to include resolution evaluation in the ield calibration process. In this study, MTF, point spread unction, and resolving power were used as measures o quality. High eiciency and objectivity were achieved by automated measurement methods.

6 spsf (pixel) spsf (pixel) Red : y =.1263x c: y =.1318x c R2 =.448 R2 =.666 Linear (c) Linear () : y = -.174x R2 =.21 : y = -.33x R2 =.3246 Green c: y =.16x R2 = Blue c: y = -.47x R2 = : y =.1165x R2 =.13 NIR c: y =.2717x R2 =.2926 AUTHOR CONTRIBUTIONS c Linear (c) Linear () c Linear (c) Linear () c Linear (c) Linear () Figure 1. RP (1%MTF) o the color channels spsf, orig: y =.28x restor: y =.19x R2 =.2983 R2 = spsf, orig: y =.28x restor: y =.29x R2 =.525 R2 =.474 original restored Linear (original) Linear (restored) original restored Linear (original) Linear (restored) Figure 11. Eect o image restoration on σ PSF. E. Honkavaara designed the empirical tests, supervised the development o the methods at the FGI, perormed most o the analysis and compiled the text. J. Jaakkola is the author o the RESOL sotware (Section 2.2), and he perormed all the empirical measurements at the FGI and participated in the data analysis. L. Markelin took care o the processing o the DMC images and helped to develop the MTF method (Section 2.2.2). S. Becker gave the details o the Stuttgart method or MTF determination, which ormed the basis o the MTF method (Section 2.2.2), and perormed the empirical study in Section 3.5. ACKNOWLEDGEMENTS The test lights were perormed in co-operation with the National Land Survey o Finland (NLS), whose support and valuable comments are greatly appreciated. Particularly the assistance given by several individuals at the FGI is appreciated. Intergraph is acknowledged or their comments concerning the results and or providing inormation on technical details o the DMC. REFERENCES Ahokas E., Kuittinen R., Jaakkola J, 2. A system to control the spatial quality o analog and digital aerial images. International Archives o Photogrammetry and Remote Sensing, Vol. 33. Pp Becker, S., Haala, N., Reulke, R., 25. Determination and Improvement o Spatial Resolution or Digital Aerial Images. In proceedings o ISPRS Hannover Workshop High-Resolution Earth Imaging or Geospatial Inormation. On CD. Becker, S., Haala, N., Honkavaara, E., Markelin, L., 26. Image restoration or resolution improvement o digital aerial images: A comparison o large ormat digital cameras. This proceedings. Coltman, J. W., The speciication o image properties by response to sine wave input, Journal o the Optical Society o America, Vol. 44, No. 6, pp Hakkarainen, J., Resolving power o aerial photographs. Surveying Science in Finland, 1986, no. 2, pp Hinz, A., Dörstel, C., Heier, H., 2. Digital Modular Camera: System Concept and Data Processing Worklow. International Archives o Photogrammetry and Remote Sensing, Vol 33, Part B2, pp Honkavaara, E., Jaakkola, J., Markelin, L., Peltoniemi, J., Ahokas, E., Becker, S., 26. Complete photogrammetric system calibration and evaluation in the Sjökulla test ield case study with DMC, Proceedings o EuroSDR Commission I and ISPRS Working Group 1/3 Workshop EuroCOW 26, CD-ROM, 6 pages. Kuittinen R., Ahokas E., Högholen A., Laaksonen J, Test-ield or Aerial Photography. The Photogrammetric Journal o Finland. Vol. 14, No 1, pp Kuittinen, R,. Ahokas, E., Järvelin, P., Transportable testbar targets and microdensitometer measurements a method to control the quality o aerial imagery. International Archives o Photogrammetry and Remote Sensing, Vol. 31, Part B1, pp Read, R.E, Graham, R.W., (22). Manual o Air Survey: Primary Data Acquisition. Whittles Publishing, Caithness, 48 p.

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