Radiometric Corrections for Multispectral Airborne Video Imagery

A. Edirlsinghe, G.E. Chapman, and J.P. Louis

Abstract images as well as facilitating good image mosaicking applica- Radiometric fidelity of calibrated airborne video imagery is tions. The vignetting of airborne video camera systems has been important if the imagery is to be used for quantitative analysis studied. King (1991; 1992) and Pellikka (1998)have suggested of target surfaces. A four-channel Multispectral Airborne Video some methods for correction of such vignetting. The magnitude System (MAvS) is used at Charles Sturt University (CSU)for a of vignetting-related radiometric distortions varies consider- range of environmenfal and agricultural monitoring applica- ably with operational system settings such as lens aperture. The tions. The radiometric distortions in the MAVSimagery could objective of this paper is to present the methodology and occur because of lens characteristics in the form of vignetting details of development, of a range of correction procedures to effects and optical aberrations. This paper details the control remove vignetting related radiometric distortions from the experiments conducted to detect and quantify such distortions. MAVS imagery, and to assess the accuracy of the results of these The vignetting in particular is shown to be creating a non- procedures. uniform brightness level across the MAVS imagery. The paper then develops efficient procedures to correct the vignetting in Abedom and Radlometrlc Mstoltlons In the MAVS Imagery the MAVS imagery by producing relevant correction coefticients, In practice, there can be many optical distortions arising from templates, and equations. The accumcy of these de-vignetting the camera lens geometry of a video imaging system. Generally, (correction) procedures is shown to be comparable to the ac- only a part of the light emitted by a point on the object plane, cumcy of similar corrections reported elsewhere. An investi- and which falls on the entrance aperture of the lens, emerges gation into the effect of spectrum related vignetting on the from the lens system and falls on a single point in the image MAVS imagery due to spectral filter characteristics found plane. This is true even for an ideally thin and perfectly spheri- negligible distortions that did not warrant corrections. This cal lens, where rays striking the outer portions of the lens focus particular type of vignetting is usually caused by the wave- closer to the lens than the more central rays. This is called length ships in the band-pass window of a filter at large spherical aberration. Chromatic aberration results in light of incident angles. different wavelengths being focused in different planes. Astig- matism arises where there is a different focal length in the verti- Introduction cal and the horizontal planes, and occurs when rays strike the The process of deriving quantitative rather than qualitative lens off center. Light rays striking the lens diagonally may pro- data from calibrated spaceborne or airborne sensors demands duce comet shaped focal spots known as aberration coma. In a high radiometric accuracy in addition to maintaining geomet- some cases the set of focal points corresponding to all the points ric fidelity of the imagery. For these sensor systems to achieve in the object plane do not form a perfectly flat image plane, pro- their full potential, particularly for multi-temporal studies, it is ducing an aberration called curvature of the field. important that radiometric correction procedures such as de- Due to the small MAvS field of view (FOV)(28"), and the use vignetting procedures be developed to improve the quality and of relatively smaller size apertures (fl1.7 to fl2.3) when acquir- consistency of system response. Presently, among remote sensing the airborne video imagery, the rays passing through the ing systems, multispectral airborne video systems are widely lenses are all close to the optical axis of the system. Therefore, used as operational remote sensing tools, due to their high spa- the use of the outer portions of the lenses is minimized and, tial and flexible spectral resolutions (Edirisinghe et al., 1999). consequently, spherical aberration, coma, astigmatism, and The four-band (blue, green, red, and near-infrared) Multispec- field curvature effects are minimal. The chromatic aberration tral Airborne Video System (MAVS) at Charles Sturt University within a band is limited to the 25-nm (narrow band) wave- (CSU) has been operationally monitoring land and water targets length difference, However, the interband chromatic aberration for a number of years (McKenzie et al., 1992;Louis et al., 1995). may be significant if the four MAVS spectral bands are not prop- A schematic diagram of the MAVS is shown in Figure 1, and the erly registered in a composite image. This can be minimized by main sensor characteristics of the MAVS (Edirisinghe et al., camera alignment, geometric correction, and digital registra- 1999;Edirisinghe, 1997) are summarized in Table 1. A 12-mm tion (Edirisinghe, 1997).Consequently, the total effects of these focal length lens is used with each of the four MAv~spectral optical aberrations on the radiometry of most of the airborne bands for normal operations. video imagery is negligible. Full radiometric correction significantly reduces image-to- Radiometric distortion is the appearance of some pixels in image brightness variation in airborne multispectral imagery, the video frame image with false brightness values causing a allowing meaningful radiometric comparison among different

A. Edirisinghe is with CCMAR, CSIRO Animal Production, PMB Photogrammetric Engineering & Remote Sensing PO, Wembley, WA 6014, Australia ([email protected],au). Vol. 67, No. 8, August 2001, pp. 915-922. G.E. Chapman and J.P. Louis are with the Spatial Analysis 0099-1112/01/670&915$3.00/0 Research Group, Charles Sturt University, Wagga Wagga, NSW, O 2001 American Society for Photogrammetry 2678, Australia. and Remote Sensing

PHOTOORAMMETRIC ENGINEERING & REMOTE SENSING August 200I 9s

-- I light that passes through the aperture. Light fall-off is a combination of two factors: the cos4 Blaw of illuminance and vignetting, where Bis the incident angle (Ray, 1988). The theoretical limit of the cos4 Blaw characterizes the geometrical and optical basis for the reduction of light in the periphery of the imagery according to central projection geometry (Ray, 1988). A simple derivation of the cos4 Blaw for an optical system can be found in Schreiber (1993). Light fall-off in digital imagery can analogously be modeled by a cos4 Blaw of illumination reduction from the center to the edge of the image, where Bis the angular deviation of a target pixel from the optical axis of the system. vignetting in an optical system occurs due to light absorption by lens walls and internal shadowing of off-axis light by components of the lens (Slater, 1980). The effect of vignetting is significant for lenses with large apertures. Vignetting is the net effect of the two independent processes known as optical vignetting and mechanical vignetting (Ray, 1988). The cos4 B VGA Vista Switcher reduction of light in the periphery of the imagery is termed natural vignetting (Ray, 1988). Therefore, the total effect of light fall-off can be described by the net effect of the three types of vignetting known as natural vignetting, optical vignetting, and mechanical vignetting. This description allows the term "light fall-off" to be replaced with the term "vignetting" in general. In the remainder of this paper, unless the terms natural, optical, or Figure 1. Schematic diagram of the MAVS. mechanical are used in conjunction with the word vignetting to describe specific cases of vignetting, the word vignetting in general refers to the total effect of light fall-off in the periphery of the imagery. spatially non-uniform response across the sensor FOv. In the Optical vignetting is caused by the reduction of the cross- case of the MAVS imagery, the sources of these radiometric dis- sectional area of an oblique beam traversing the lens in com- tortions are the atmosphere between the target and the sensor, parison to that of an equivalent axial beam. The effect of this is problems in the video signal digitization phase (e.g., low sig- a reduction in image illumination, due to physical length of the nal-to-noise ratio or inadequate sampling frequency rate), sun lens, the position of the aperture stop, and the diameter of the anglelview angle (reflectance) variations, cover-type bright- front and rear elements (Ray, 1988). The magnitude may be ness variation, non-uniform response due to defective sensor estimated by projecting the image of the stop and rear element elements (missing pixels) or image plane misalignment, and in the object space onto the front element. This reduction of vignetting. Generally, the full radiometric calibration of a illumination in the imagery is also known as "cat's-eye effect." remote sensing system addresses the problem of securing the The amount of vignetting depends on the f number in use; for radiometric fidelity of an imaging system. This includes radio- an aperture with high f number, the optical vignetting is mini- metric corrections such as vignetting corrections and bi-direc- mal while, for an aperture with low f number, the effect of opti- tional reflectance variation corrections, as well as establishing cal vignetting may be high. absolute radiometric calibration or building relationships Mechanical vignetting is caused by mechanical features of between radiometric response of the system and actual the lens intruding into the Fov, causing some peripheral dark- reflectancelradiance received by the sensors. This paper ening of the image due to absorption by the lens walls (Ray, addresses the problem of vignetting in the MAVS imagery and its 1988). This can be the rim of a lens hood that is too long or of correction. The radiometric calibration of the airborne video the wrong aspect ratio. Often, a filter holder may be too deep. system has been dealt with elsewhere (Edirisinghe, 1997;Ediri- This problem is more severe with wide-angle lenses. singhe et al., 1999). Natural vignetting is expected to be present in any optical system, even those with an ideal thin lens. It is also reported Radiometric Diaortlon Due to Radial Ught FalM(Ylgnettlng) (Ray, 1988) that a standard lens with an FOV of 52" has a periph- The systematic light fall-off in lens-based imaging systems eral illuminance of only two-thirds the axial value and, for an reduces the brightness of the image radially from the center to extremely wide-angle lens with the semi-field angle of 60°, the the edge. This is mainly caused by the optical system and lens peripheral illumination is only 0.06 of its axial value. King characteristics. The light fall-off appears as concentric shade (1992)reports a vignetting variation on the order of cos4 Bin the variation in the imagery and is a major radiometric distortion linear regression, between Cand cos4 Bwhere Cis the ratio of common in videography. It is produced by an optical system the brightness at the angle Bto the central brightness at 8 = 0'. that fails to equally transmit, at higher incident angles, all the He also notes that only for large apertures does this linear rela-

TABLE1. MAVS RADIOMETRICRESPONSE CHARACTERISTICS IN THE BLUE,GREEN, RED, AND NEAR-INFRAREDSPECTRAL BANDS Dark Current System Noise Dynamic Range SignallNoise Ratio-SIN Radiometric Band (DN) (DN) (DN) (dB) Precision IDNl. . Blue 12 0.90 243 56.60 135.00 Green 12 0.76 243 48.60 157.80 Red 13 0.80 242 49.60 151.30 MR 13 0.92 242 48.40 131.50

916 August 2001 PHOTOORAMMETRIC ENGINEERING & REMOTE SENSING tionship have a non-zero offset. Vignetting effects can also be on analytical expressions characterizing the pattern of bright- reduced from an order of cos4 Bdependence to an order of cos3 ness change across the imagery and are applied as a digital cor- Bby using lens design techniques such as quasi-symmetrical rection process. In digital correction of vignetting in video- types with short back focus and retrofocus lenses (Ray, 1988). graphic imagery, the off-axis DNs are normalized to the vignett- Modern lens designs allow the vignetting to be further reduced ing free DN values in the center of the video frame using imagery to less than cos 8. Generally, vignetting will be small for optical of uniform Lambertian surfaces (Neale et al., 1994). systems with small aperture openings. The correction of the combined effect of vignetting and In practical cases, with thick lenses, the illumination will cover type brightness variations, instead of using the separate fall-off even more rapidly due to the combined effects of natu- corrections, is another technique for controlling the problem of ral, optical, and mechanical vignetting. The amount of vignett- overall spatial non-uniformity. The band ratio technique has ing in a given camera may vary with the focal length, lens, been used by King (1991) to reduce a cover type brightness vari- aperture setting, form of the camera, and spectral filter used. ation of 212 percent, including the vignetting, on either side of Another type of vignetting that distorts the radiometric nadir, to less than 5 percent for image classification purposes. fidelity of video imagery is spectrum-related vignetting. It is typically introduced at larger incident angles by an interference filter located in front of a lens (Mao et al., 1995). With this Detection of the MAYS Lens Vignetting design of filter placement, the band-pass window of the filter Method of the Experiment tends to shift towards the lower wavelength more than the shift The measurements of the MAVs camera lens vignetting con- which would be expected in the case where the filter is located ducted in the field used a 3- by 3-m grey polyester sheet imaged at the back of the lens. The shift creates a slight error in the spec- under uniform solar illumination conditions. This sheet was tral information at the periphery of the image, which should be i laced on a flat mass surface 4 meters below the MAVS and rectified accordingly. *hagedwith ea& camera. The operational apertures for the The theoretical basis for this phenomenon of filter experiment were selected to avoid saturation of the video sig- response frequency shift is the non-uniform absorption of light nai from the target. The target produced a uniform reflectance by the interference filters with different incident angles. This with less than 3 percent random variation of brightness across effect of filter absorption is characterized by Mao et al. (1995) the whole surface. using the following formula for transmittance: In an ideal situation with a uniformly reflective target, if the image in question is not affected by vignetting distortions, a uniform brightness level is expected across the whole Fov. It is assumed that any radially dependent deviation (reduction) of the reflectance in the target image in this case is due to the effects of vignetting. This is the basis on which the corrective where Qti and Qm are transmitted incident energies at an angle 8 procedures are developed to eliminate the vignetting dis- and at normal incidence to the filter, respectively, Pis the tortions. absorption coefficient of the filter; dfis the thickness of the fil- It is known that, due to the difference in the illumination ter; and n, is the effective refractive index of the filter glass. P levels, the apertures operational in the laboratory environment strictly depends on the wavelength (A). As the value of Qti are not suitable for field use. However, field apertures may be changes with the change of Band P, the corresponding image used for airborne applications provided the solar illumination brightness (DN) is changed. level does not change significantly. Therefore, a vignetting However, A is a function of 19 and the wavelength shift in experiment performed in the field, with a particular aperture, the band centre is given as (Mao eta].,1995) has the advantage that any vignetting effect observed in the field with normal solar illumination would be closer to that expected for airborne images with the same aperture. Hence, any correction scheme developed to rectify the field based vignetting patterns is readily applicable to airborne imagery. where n, is the refractive index of the external medium, A. is the peak wavelength of the band-pass window at normal inci- Observations dence or B = 0°, and A is the shifted peak at an incident angle As a result of this experiment the faint vignetting patterns of B f 0". It is also evident from Equation 2 that the band-pass MAVS imagery in blue, green, red, and NIR spectral bands were window will shift towards the shorter wavelengths (A < Ao) detected as shown in Figures 2a to 2d. with increasing 0. This shift is principally caused as a result of For medium level MAVS apertures between fl2.4 and fll.7, absorption of light in the interference filter by multilayers of vignetting effects are found to cause brightness reductions of thin films. Hence, it is evident from Equations 1and 2 that the 14 percent and 8 percent from the center to the edge of the off-axis rays going through the interference filters are subject to image, for the horizontal and vertical video directions, respec- spectral and transmission (absorption) changes causing unde- tively. It is assumed that the center of the image is free from sirable brightness variations across the imagery. vignetting effects and, as a result of this, the edges are com- Quantitative assessment on target surfaces through air- pared to the center brightness. For these medium apertures, the borne video imagery demands a reasonable level of radiomet- brightness reduction pattern conforms to the cos4 Blaw of natu- ric correction for inherent vignetting effects. Severe cases of ral vignetting for the MAVS with FOVS of 28' and 22" in the hori- vignetting may disturb even a basic visual interpretation of the zontal and vertical video directions, respectively. It has been imagery. observed that, with larger apertures such as f11.4, the center to Vignetting in optical systems can be suppressed by using edge brightness difference due to vignetting is radially in- antivignetting filters, which are designed to compensate for creased by up to 36 percent and no longer follows a cos4 Blaw. variation in light intensity on the sensor element as a function These observations demonstrate that (1)the dependence of the of focal length variation from the optical center to the edge of vignetting pattern on the operational aperture, and (2), for the imagery (Roberts, 1995). larger apertures with fl1.7 and above, the radial reduction of The correction of vignetting distortions is also known as brightness from the center to the edge of the image is somewhat de-vignetting. Usually, the de-vignetting algorithms are based more than that predicted by the cos4 Border. This appeared to be

I PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING could be modeled by a linear function of the brightness value (DN) versus view zenith angle. This angle for each individual pixel of the image is defined as a function of corresponding x and y coordinates.

Correction of the MAVS Lens VignettlngStatlstlcaI Approach Method of the Correction There is a slight decentering effect visible in the images of each biAVs spectral band with aperture opening larger than f 11.8. In the case of the MAVS blue-band imagery with this aperture group, the optical center at the pixel coordinates (354,304) is easily recognizable by the hot spot in the center of the bright circular area. Figure 2a shows this effect for a MAV~blue-band image with aperture fh.4. It is slightly shifted towards the fourth quadrant from the geometric center (369,288) of the image. This could be due to a small misalignment of the CcD element array, i.e., it is not at right angles to the optical axis, or due to an increased non-symmetric type of mechanical vignetting, or both. Interestingly, images of the same target, taken with smaller aperture openings (fl2.1), show no visible shift in their bright centers in any of the MAVS spectral bands. Hence, the vignetting correction procedures for images with the large aperture group with f11.7 and above are developed in relation to the optical center rather than the geometric center. Data from a field-based biA~simage with the maximum aperture f 11.4 (for the large aperture group) and aperture f 12.1 (for the small aperture group) are used for the development of a vignetting correction procedure in this paper. Mean digital numbers for each 50 by 50 non-overlapping rectangular pixel area are used for the analysis. These rectangles are located along two perpendicular center lines of the image in the horizontal and vertical video directions. The angle 6in this procedure is Figure 2. Vignetting in the MAVS images defined from the optical center to the center of each sample area with aperture f/1.4 (a to d), their respec- in both the x or y directions. tive correction templates (e to h) for spec- The vignetting data in the blue-band imagery with aperture tral bands blue, green, red, and NIR, f 11.4 and red-band imagery with aperture fh.1are presented respectively, and vignettingcorrected in Tables 2 and 3 to represent different wavelength band and MAVS blue-band imagery with aperture f/ aperture combinations. These tables give the incident angle B 1.4 (i-statistical method and j-template at the center for each 50 by 50 non-overlapping pixel area sam- based method). ple, cos4 8, x or ycoordinate value of the sample center, sample mean (DN)for different Balong the horizontal and vertical image directions, and the coefficient of reduction of brightness for blue and red spectral bands Cb and C,, respectively, along the horizontal and vertical video directions. The values of Cb and the result of increased mechanical vignetting at higher aper- C,are calculated by dividing the sample mean at Bby the mean ture settings. of the sample at the optical center. In addition, the peripheral brightness of the images in the For any MAVs band, the coefficient of brightness reduction blue, green, red, and NIRbands, with aperture fll.4, in the hori- can commonly be written as C, with irepresenting B, G, R, or NIR zontal video direction is reduced up to the 64 percent, 75 per- NIR cent, 78 percent, and 76 percent level, respectively, due to for the blue, green, red, and bands, respectively. vignetting. By analyzing the images acquired in the field, we clearly Results identified the increasing effects of vignetting on images This investigation showed a maximum brightness variation of acquired with apertures above f 11.8 belonging to the large aper- 36 percent on either side of the image optical center along the ture group. This trend is evident for all four bands even though horizontal video direction in the MAW blue band for the images band-to-band minor dissimilarities were present. The above of aperture f 11.4. The average digital number is calculated for observation shows that two vignetting correction approaches images over the 50- by 50-pixel areas along the video x (hori- need to be developed for the MAVS imagery of these two distinc- zontal) axis. tive aperture groups. It is clear, from data presented in Tables 2 and 3, that the Also, within these two broad aperture classes, vignetting value of Cbis smaller (i.e., brightness reduction is greater) than was found to be dependent on the aperturelspectral filter com- the respective cos4 @valueat the edges of the image. This indi- bination in each camera. Thus, the resulting correction parame- cates the existence of other forms of vignetting such as ters and procedures derived for a pdticular combination of mechanical and optical vignetting, in addition to natural aperturelfilter in the field experiment can only be applied to vignetting, in the images of this aperture group. Thus, the cos4 airborne images of the same combination. Bcorrection, which targets the natural vignetting distortions, is Statistical analysis of the data from the field experiment inadequate for the MAVS images of the large aperture group. proved that the pattern of vignetting in the large aperture group However, in the case of aperture f12.1, vignetting distortions in

918 August 2001 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING TABLE2. MEANSOF 50- BY ~GPIXELSAMPLES ALONG THE HORIZONTALIMAGE AXIS AT GIVEN~NCIDENT ANGLES (0) OR GIVENXCOORDINATES FOR THE BLUEBAND WITH APERTUREf/1.4 AND RED BANDWITH APERTUREf/2.1 00 -13.8 -11.7 -10.0 -7.6 -5.2 -2 0 +2.2 +5 +7.3 +9 +11 +12.7 +14.6 - -- cos4 0 0.89 0.92 0.94 0.97 0.98 0.99 1.00 0.99 0.98 0.97 0.95 0.93 0.91 0.88 x-coordinate 25 60 104 164 224 304 354 408 480 536 580 628 672 720 MeanDN;(fll.4)-blue 110 116 122 132 140 146 152 146 140 134 122 116 108 100 Mean DM,( fl2.l)-red 56 62 61 63 65 64 65 65 64 62 62 60 59 58 cb-(fl1.4) 0.72 0.76 0.80 0.87 0.92 0.96 1.00 0.96 0.92 0.88 0.80 0.76 0.71 0.66 Ci(fI2.1) 0.86 0.95 0.93 0.97 1 0.99 1.00 1.00 0.99 0.96 0.96 0.93 0.91 0.89 +Indicates to the right of the image center in the blue band -Indicates to the left of the image center in the blue band

TABLE3. MEANSOF 50. BY PIXEL SAMPLESALONG THE VERTICALIMAGE AXIS AT GIVEN~NCIDENT ANGLES (8) OR GIVENY-COORDINATES FOR THE BLUEBAND WlTH APERTURE f/1.4 AND RED BAND WlTH APERTUREf/2.1 O0 +11.4 f9.5 + 7.6 +5.0 +2.3 0 -1.7 -4.6 -7.0 -9.8 cos4 8 0.92 0.95 0.97 0.98 0.99 1.00 0.99 0.98 0.97 0.94 y-coordinate 25 66 114 180 246 304 346 420 478 548 Mean DN;(fll.4)-blue 119 122 129 136 148 152 148 140 132 125 Mean DN;(fl2.1)-red 59 61 63 63 65 65 65 62 63 60 Cb-(f11.4) 0.78 0.80 0.85 0.89 0.97 1.00 0.97 0.92 0.87 0.82 cf(fl2.1) 0.90 0.93 0.97 0.97 1.00 1.00 1.00 0.96 0.97 0.91 +Indicates above the image center in the blue band -Indicates below the image center in the blue band

the both horizontal and vertical directions substantially agree with the cos4 Bmodel. In the case of aperture fl1.4, it is found that the pattern of vignetting distortion along the x or y direction from the optical where ZC(x,y) and ax,y) are corrected and distorted pixel values center to the edge of the image can be well approximated with a (DN), respectively, and Xob= 354 and Yob = 304 are the optical linear equation. The form of the equation in the horizontal direc- center x and y coordinates, respectively. This equation is tion is Cb(x)and in the vertical direction Cb(y) for the blue band. applied to every pixel of the distorted blue-band image line by The radial nature of the distortions allows the fitting of the line, starting at the origin (0,O). The above parametric correc- same linear equation for all other directions emanating from the tion procedure enables the vignetting effects to be reduced optical center. The equations of the form Cb(z),where z = from 36 percent to 4 percent of the center brightness for this ,/-, ,/-, can be represented in general form with slope (Pb) band with the aperture f 11.4 (see Figure 2i). Vignetting in the other three MAVS bands for this aperture group can similarly be and offset (a)parameters as follows: corrected using Equation 4 with corresponding parameters of Pi, a,,Xoi ,and Yo,, with i representing G, R, or NIR for the green, red, or MR spectral bands, respectively. This result compares well with the result of the band ratio technique (King 1991) The values of Pb and Qb obtained using linear regression used to reduce the 212 percent brightness variation to less analysis are given in Table 4. In this table, the column with than 5 percent. heading MRS provides the Multiple R-Squared coefficient (r2) The red-band data in Tables 2 and 3 for aperture f 12.1, rep- for each horizontal and vertical video direction. The radial resenting the small aperture group (fl1.8 to f/2.2), show a 14 nature of the distortion pattern of vignetting results in statisti- percent and 8 percent brightness reduction in the periphery of cally similar values for Pband Qbbeing obtained for x (left and the image in the vertical and horizontal directions, respec- right from the center) and y (top and bottom from the center) tively. The result of linear regression between vignetting- directions. This suggests that similar values of Pband Qbcan be affected DN for this aperture, from Tables 2 and 3 (combined), expected for all other directions emanating from the center in a versus the corresponding cos4 8, is given in Figure 3. The range radial manner. Then the vignetting correction for the whole of estimated values of slope (67) and offset (-2) for this regres- image can be applied using the parameters derived from the x sion line (r2= 0.88) with standard errors of k5.5 and 25.2, and y directions. respectively, compare well with the slope of 65 and offset of 0, Good vignetting corrections for aperture f 11.4 in the blue expected in the case if vignetting is directly proportional to cos4 band can be obtained using Pb = 0.0008 and the average value 8. The above deviation of slope and offset is influenced by the of Qb = 0.76 calculated from Table 4 and rewriting Equation 3 standard error of sample brightness (+ 3 DN)in Tables 2 and 3. in terms of raw pixel coordinates as This variation in sample brightness is caused by the error (less than 3 percent) in surface uniformity of the target and the MAVS red-band radiometric uncertainty given in Table 1. Hence, TABLE4. LINEARLEAST-SQUARES REGRESSION RESULTS OFTHE EQUATION these observations point to a cos4 B order vignetting for the FI~DTO THE VIGNEITINGDISTORTIONS OF THE IMAGES OF THE BLUEBAND small aperture group. WITH APERTUREf/1.4 Vignetting in this group can be corrected to an acceptable MRS Pb Std. Error.for Pb Qb Std. Ehor for Qb level of accuracy (95 percent), simply by multiplying each individual pixel value in the image by the corresponding COS-~ Horizontal 0.99 0.0008 0.00003 0.72 0.07 0.01 8value for that pixel. In this case, the vignetting correction can Vertical 0.95 0.0008 0.00008 0.79 be simply written as

I PHOTOQRAMMETRIC ENGINEERING & REMOTE SENSING August 2001 919 target surface, which may cause brightness alteration to the 66 y = 67.054~-2.024 pure vignetting patterns. The template for the MAVSblue, green, 65 R' = 0.8745 red, and NIR bands in Figures 2e to 2h are created according to 64 - Neale and Crowther (1994). p- g 62 - Results The template-based vignetting corrections carried out for the 1::- MAVS test imagery improved the peripheral brightness from 64 a 5s - percent of the undistorted center brightness level up to the brightness level of the center (see Figure Zj), where the effects B s- of vignetting are assumed negligible. This outcome also is com- 57 - parable to the accuracy reported (Neale and Crowther, 1994) 58 - for a similar type of correction approach. For the MAVS test 55 s imagery, this result is better than the result from the statistical 0.86 0.88 0.S 0.92 0.94 0.M 0.98 1 1.02 method (Figure 2i). However, the presence of undesirable co~"4(Theh) regions with non-uniformities of up to 4 percent of the center Figure 3. Result of the regression between vignetting brightness level are observed across the corrected test imagery (see Figure 2j), making the overall accuracy about 96 percent. affected DN versus cos^4(~heta)(cos4 8)for aperture f/2.1. This non-smooth brightness distribution across the corrected imagery is caused by the propagation of non-smooth template characteristics due to the convolution operation conducted between the template and the target image as well as due to the non-flat nature of the target surface. The non-smooth template characteristics are inherited from the non-perfect test target used for its creation. Therefore, the correction accuracy in this where method is completely dependent on the quality of the surface of the test target used to create the reference image before the templates are generated. Special care must be taken in producing test targets for laboratory or field use so that error-free tem- and Ic(x,y) and I(x, y) are the corrected and distorted pixel val- plates can be used for vignetting corrections. It is difficult in ues [DN),respectively. In this case, the observation angle @is practice to produce a perfectly uniform test target to cover the measured from the geometric center (369,288) of the image to full FOV of the system due to non-ideal characteristics of practi- the target pixel because there is no separate optical center iden- cal surfaces. A major disadvantage of the template-based tech- tifiable in the MAVS imagery. nique is the requirement for additional disk space for storage of Equation 5 is applicable to every pixel of the distorted all possible correction templates for different operational aper- imagery belonging to any of the MAVs spectral bands, line by tures. It is also found that the spatial non-uniformity in the line, starting at the origin (0,O). MAVS images belonging to the large aperture group is not per- Because no additional parameters are involved in the cal- fectly radial. The distortion pattern is complex, and fitting a culation, the implementation is simple and fast. The cos4 Bcor- linear statistical model failed to completely characterize all the rection reduces the vignetting in the periphery of the images variations in it. The application of the template-based correc- from 14 percent to less than 5 percent, for this group of aper- tion in this case produces faster results and a slightly better tures, making them comparable to the correction of the MAVS level of accuracy than with the statistical method. large aperture group as well as king's (1991) vignetting correction level. MAVS Spectral Rlter Response ShWt for Off-Axis Rays Correction of the MAVS Lens Vlgnetting-TemplateBased Method of the Experiment Mao et al. (1995) suggested that the optimal location of the Approach interference filter is at the back of the lenses rather than in front Method of the Comedon of the lens in order to minimize the visual appearance of Neale and Crowther (1994) have suggested the use of a bright- vignetting and reduce the shift in the band-pass wavelengths. ness correction coefficient matrix or a template image in Their conclusion was that, in order to completely correct for the vignetting corrections. The template is a digitally stored vignetting effect, it is necessary to combine the optimal filter inverse or correction coefficient matrix of the brightness placement with a digital brightness correction scheme using an reduction function caused by the vignetting. The idea is to cre- analytical model. However, for a system like with the ate a template image of every operational bandlapertwe com- interference filters already fitted in front of the lenses and in bination. Then the target image is digitally convolved with the which the filters cannot be practically placed at the back of the template image of the corresponding combination for the correc- camera, the digital correction of vignetting is the only option. tion of vignetting effects. Theoretically, this method has the We also believe that the shift in the band-pass wavelength is capacity to correct the problem of vignetting completely pro- less important for the wide band-pass filters (24 nm) used for vided a perfect template is used. the MAVS. Our approach to this type of vignetting is that the A field experiment was conducted to create test images for shift in the band-pass wavelength must be taken into account template generation and accuracy assessment. The similarity on the basis of its proportionality to the total bandwidth of the of the illumination conditions allows the use of the same tem- filter. If the shift is large enough to distort the spectral informa- plates for airborne images with the same apertures. A cherry- tion at the periphery of the imagery, there is no alternative but picker was used to hold the camera box of the MAVS above a suf- to reduce the effect by optimally re-positioning the filter as ficiently flat uniform grey target on a clear day, in order to described above. The digital correction alone in this case is acquire the test images for this Durpose. The flatness of the tar- ineffective, because it does not have control over the spectral get's minimizes the possibility of biightness variation across the changes. However, if it can be shown that the spectral shift in imagery due to bi-directional reflectance variation across the the band-pass is sufficiently small relative to the width of the

920 August 2001 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING band, then the average spectral response of the band will not the center wavelength of the MAVS interference filters are 3,6, be affected by the shift. In this case, it is quite reasonable to 7.5, and 9 nm for the blue, green, red, and NIRbands, respec- carry out a vignetting correction on the basis of digital proc- tively. The increase in the amount of wavelength shift shown in essing using an analytical expression as discussed earlier or Figure 4, for a given incident angle (14"),from the blue band to using corrective templates as detailed in the preceding section. the NIR band, agrees with Equation 2. It is also important to investigate the overall signal response This shift is characterized by a filter response variation, levels at the full width of the band with regard to this wave- causing a change in the radiometric and spectral properties of length shift. If the drop in the center peak response due to the the rays going through the filter at large incident angles. As a wavelength shift is significant with regard to the actual vignett- result of this, brightness and spectral distortions occur in the ing levels, then the digital correction scheme can still take into off-axis regions of the image. These distortions are non-uniform account this change as a part of the total vignetting effect and across the image due to the dependency on the angle of correct accordingly. incidence. The four MAVS filters have been investigated in the labora- Importantly, each shifted spectral band center in the above tory for possible band-pass shift with changing incident angle case, for an incident angle of 14", is well within the full-width (8) using an Analytical Spectral Devices' Personal Spectrome- half-maximum (FWHM) of the reference response curve at O0 ter (PSII), which is a calibrated hand-held radiometer opera- incidence for the corresponding band. It is noted here that each tional in the spectral range of 350 nm to 1100 nm over 512 of these MAVS reference response curves has a 24-nm full band- channels, each having a band width of 1.5 nm. In the case of width. The average spectral effect for the whole band is there- MAVS, the maximum evariation is 14" or half of the maximum fore not significantly different from the spectral average of the FOV (28").Each MAVS interference filter was in turn placed ver- full band with paraxial rays. tically on a spectrometer table, which was aligned with a white If we compare the percentage reduction of the peak inten- light source. The hand-held radiometer PSI1 with 10"foreoptic sity due to the band center shift given above with the maxi- was also attached to the spectrometer. The PSII was mounted mum measured vignetting effect of 36 percent at the periphery behind the filter so that the light transmitted through the inter- of the image (blue band, aperture f ll.4), the former is negligi- ference filter can be measured and recorded as required. The bly small. On the other hand, the maximum response accuracy spectrometer table may be precisely rotated to any desired 8 levels of about 95 percent achieved under the vignetting correc- value for the interference filter, and the corresponding trans- tion procedures presented earlier are unable to correct for the mitted light intensity was then measured by the radiometer. remaining response loss of about 5 percent. This applies even if the response loss due to wavelength shift in the MAVS spectral Results and Discussion bands (which is a few percent in each band) is properly cor- The laboratory-based experimental results, shown in Figure 4, rected before the vignetting procedures are carried out. A digi- show the MAVS interference filter response curves for different tal correction scheme would therefore correct for the intensity incident angles (8) up to 30". The maximum operational inci- drop-off in any case, regardless of whether this reduction is dent angle in the case of the MAVs is 14". For a 8 of 14", the actually caused by band shift or real vignetting. results indicate a 3.9 percent, 2.1 percent, 4.8 percent, and 2.3 Based on this experimental evidence, we expect the band percent peak response reduction for the blue, green, red, and center shift to be sufficiently small, and not to change the aver- NIR spectral bands, respectively. The response changes in the age spectral properties of the MAVS acquired imagery for MAVS imagery for smaller incident angles are less than these remotely sensed targets. It shows that the digital processing as values. outlined earlier is adequate to correct the problem and does no? The wavelength-calibrated PSII with + 1-nm accuracy is require special placement of the filter for the MAVS spectral used to measure the MAVS filter bandwidths and center wave- bands. lengths for each of the four filters. These are then compared with the following manufacturer's band center specifications Conclusion of 460 nm for blue, 550 nm for green, 650 nrn for red, and 770 The presence of radiometric and geometric distortions is detri- nm for NIR bands. mental to applications of airborne videography. The problems The experimental results in Figure 4 also show that, for off- associated with radiometric distortions in MAVS imagery have axis rays with an incident angle of 14", the band-pass shifts of been investigated. The significance of radiometric corrections is stressed, in the context of radiometrically calibrated imagery being used in quantitative data analysis. The effects of lens vignetting for the MAvS image interpreta- Blus, Green, Red and NIR spectral band-pass shifts for tions are discussed. It is shown that properly designed control lncfdent angles (Theta) of 0,8,14 and 30 dogma experiments are necessary to accurately quantify the lens- 3500 Blue Green Red NIR based vignetting in the MAVS imagery. The experimental results also indicated that the vignetting 3000 in a particular camera is dependent on the operational aperture. The type of vignetting in the MAVS images is observed to fall into two operational categories based on the aperture "flnum- ber" used. The first group, named the "larger aperture" group, ..-...Thet~=l4 E 1500 contains the images acquired with apertures greater than f 11.7, El and the other group consists of images belonging to the small lo00 g aperture group. The MAV~vignetting correction procedures are 500 developed separately to address the specific distortion charac- 0 teristics of these two groups. The maximum MAV~vignetting 350 450 550 650 750 850 error of 36 percent loss of brightness at the image periphery has Wavakngth (nm) been corrected to only a 4 percent loss. This level of vignetting reduction compares well with other reported corrections (King, Figure 4. MAVS spectral filter band-pass shifts for different 1991; Neale and Crowther, 1994). The vignetting correction incident angles (8). coefficients and templates are obtained for all possible operational bandlaperture combinations.

PHOTOGRAMMEIRIC ENGINEERING 81REMOTE SENSING August 2001 921 The influence of the band-pass response shift for the MAVS , 1992. Evaluation of Radiometric Quality, Statistical Character- interference filters was compared with off-axis rays to the over- istics, and Spatial Resolution of Multispectral Videography, The all vignetting. The experimental evidence suggests that the Society for Imaging Science and Technology, 36(4):394-404. band center shift in wavelength is small and its effect is negligi- Louis, J., D. Lamb, G. McKenzie, G. Chapman, A. Edirisinghe, I. ble on the average spectral characteristics for the width of the McCloud, and J. Pratley, 1995. Operational Use and Calibration MAvS of Airborne Video Imagery for Agricultural and Environmental spectral bands. The filter peak response reduction in Land Management Applications. Proceedings of the 15th Biennial intensity is small in this case and in any event is digitally cor- Workshop on Color Photogmphy and Air Videogmphy, Terre rected by the overall vignetting correction procedures devel- Haute, Indiana, pp. 326-333. oped in this paper. Mao, C., T. Gress, D. Kettler, and P. Mausel, 1995. Vignetting Elimina- The de-vignetting procedures developed in this study tion of Digital Video Camera Systems, Proceedings of the 15th achieved an accuracy of about 4 percent peripheral brightness Biennial Workshop on Color Photography and Air Videogmphy, decrease in the periphery of the MAVs imagery, This shows that Terre Haute, Indiana, pp. 335-345. the MAVS images can be adequately radiometrically corrected Mckenzie, G., A. Dare-Edwards, J. Louis, V. Van Der Rijt, and J. Pratley, for their internal lens distortions. 1992. Application of Low-cost Airborne Video Technology to Aus- The procedures, parameters, and templates developed in tralian Agriculture, Proceedings of the 6th Australasian Remote this paper are readily applicable to MAVS images in routine air- Sensing Conference, Wellington, New Zealand, pp. 293-297. borne missions. These methodologies are also useful in devel- Neale, C. M. U. and B. G. Crowther, 1994. An Airborne Multispectral oping respective correction procedures for the imagery of other VideoIRadiometer Remote Sensing System: Development and multispectral video systems. Calibration, Remote Sensing of Environment, 49:187-194. Pellikka, P., 1998. Development of Correction Chain for Multispectral Acknowledgment Airborne Video Camera Data for Natural Resource Assessment, The authors are grateful to the staff of the Spatial Analysis Unit Fennia, the Journal of the Geographical Society of Finland, of Charles Sturt University for their support of this research 176(1):1-110. work. Ray, S.F., 1988. Applied Photographic Optics: Imaging Systems for Photography, Film and Video, Focal Press, London and Boston, 647 p. Edirisinghe, A., 1997. Development of Radiometric and Geometric Roberts, A., 1995. Integrated MSV Airborne Remote Sensing, Canadian Correction Procedures for Low Cost Airborne Video Image Proc- Journal of Remote Sensing, 21:214-224. essing Systems, PhD thesis, Faculty of Science and Agriculture, Russ, J.C., 1992. The Image Processing Handbook, CRC Press, Boca Charles Sturt University, Wagga Wagga, NSW, Australia, 278 p. Raton, Florida, 442 p. Edirisinghe, A,, J. Louis, and G. Chapman, 1999. Radiometric Calibra- Schreiber, W.E, 1993. Fundamentals of Electronic Imaging Systems. tion of Multispectral Airborne Video Systems, International Jour- Some Aspects of Image Processing, Third Edition, Springer-Ver- nal of Remote Sensing, 20(14):2855-2870. lag, New York, Berlin, Heidelberg, 332 p. King, D., 1991. Determination and Reduction of Cover Type Brightness Slater, P.N., 1980. Remote Sensing: Optics and Optical Systems, Addi- Variations with View Angle in Airborne Multispectral Video Imag- son-Wesley, Don Mills, Canada, 575 p. ery, Photogmmmetric Engineering & Remote Sensing, 57(12):1571-1577. (Received 20 April 1999;revised and accepted 05 January 2001)

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