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Astronomical Data Analysis Software and Systems VI ASP Conference Series, Vol. 125, 1997 Gareth Hunt and H. E. Payne, eds.

Titan Image Processing
Nailong Wu and John Caldwell Dept. of Physics and Astronomy, York University, 4700 Keele St., North York, Ontario, M3J 1P3, Canada Abstract. Images of Titan by the Hubble Space Telescop e (HST) are very small in size and have very low spatial resolution. Sp ecial methods of image processing are required to extract information from these images. In this presentation, these methods are describ ed and results are rep orted.

1.

Introduction

Titan, one of the satellites of Saturn, has a planet-size solid b ody, and a thick atmosphere with molecular nitrogen as its principal constituent and with a considerable amount of methane (CH4 ) (Beatty et al. 1990). Currently, in searching for features on Titan's disk imaged by the HST PC1 detector, we are faced with two problems: (1) Low spatial resolution (Figure 1). The diameter of Titan's disk is only approximately 20 pixels. The pixel size corresp onds to ab out 290 km at the center of Titan's disk. (2) Poisson noise on Titan's disk, which makes it difficult to detect features. For example, it is imp ossible to detect a p oint source having an amplitude of 12 DN (digital numb er) and sitting on Titan's disk with a uniform pixel value of 2000 DN, b ecause the SNR (signal-to-noise ratio) is only 1.0. In contrast, it would b e easy to detect the same source if it sat on an empty background, b ecause the SNR is 13.1. The two aforementioned problems necessitate processing Titan images by sp ecial methods to extract information for analysis. Each of the methods used by us is describ ed in one of the following four sections, including the problem addressed, the method, the key computer programs (mainly in IRAF/STSDAS and IDL), and the results. In the conclusion we summarize our exp erience, and give suggestions for observing Titan in the future. 2. Image Restoration Using MEM and MLM

Problem: Limb-brightening and -darkening. The variation of brightness radially from the center of Titan to the limb is called limb-brightening or limbdarkening, dep ending on whether this variation is increasing or decreasing. Its determination is imp ortant for modeling Titan's atmosphere. Method: Remove the smoothing effect of the PSF (point spread function) of the HST. Because of this smoothing effect, limb-darkening will b e enhanced, while limb-brightening will b e weakened so that a radial profile in an observed image may app ear to b e falsely limb-darkened or neutral. Therefore, in the case of (apparent) limb-darkening, it is required to restore the image to find out 194

© Copyright 1997 Astronomical Society of the Pacific. All rights reserved.


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Figure 1. image.

A typical Titan

Figure 2.

Profiles at p osition angle 0 .

the truth. This is accomplished by deconvolution using MEM (the Maximum Entropy Method) or MLM (the Maximum Likelihood Method). Furthermore, for accurate modeling, deconvolution is advisable in any case. Programs: Two tasks in IRAF/STSDAS, mem and lucy, implement deconvolution by MEM and MLM, resp ectively, and give similar results in our case. The PSF associated with the observed image, necessary for executing these tasks, is generated by running the stand-alone program TinyTim. Results: For a CH4 image at 889 nm wavelength, out of twelve radial profiles at p osition angles 0 (Titan North), 30 , . . . , 330 , seven app ear to b e limb-brightened, while five are limb-darkened in the observed image b efore deconvolution. In contrast, after deconvolution, four (at 0 , etc.) of the latter five profiles b ecome limb-brightened, and the other is nearly flat to the limb. Three radial profiles at 0 are plotted in Figure 2 to show the effect of deconvolution. Curve fitting is used for further clarification of limb-brightening after deconvolution.

3.

Image Enhancement by Subtraction and Filtering Temporal brightness changes in images. By detecting brightness Titan images with time, we can discover transient features. The that the changes may well b e small compared with the noise, and resolution of the images is very low.

Problem: changes in difficulty is the spatial

Method: Taking differences between sequential images. Before doing this, we must interp olate the images to reduce the pixel size, and register (align) them at the subpixel level. After the subtraction op eration, we lowpass-filter (smooth) the difference images to improve SNR and eliminate small-scale fluctuations. Programs: The key tasks used in IRAF/STSDAS are: magnify for interp olation; crosscor and minmax to find the relative shifts b etween images; imshift to shift images for registration; imarith for subtraction; and gauss for lowpassfiltering (convolution).


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Figure 3. One of the six filtered difference images.

Figure 4. Bifurcation p oints in two groups of images.

Results: Two groups of images at 673 nm wavelength, with a time difference of 2d 9h 20m are processed. The groups have two and three images, resp ectively. The magnification factor is 9, i.e., the pixel size is reduced to 1 /9. The FWHM (full width at half maximum) of the Gaussian filter is 18 (reduced size) pixels. A bright area is detected in all six (2в3) difference images, b eing centered at p osition angle +8 3 with resp ect to Titan North, latitude +45 4. One of the . . six filtered difference images is shown in Figure 3. The pixel values in the bright area increased noticeably during this p eriod of time. Similar results have b een rep orted and discussed by Lorenz et al. (1995). 4. Image Enhancement by Edge Detection and Morphological Processing

Problem: Wind velocity. Measuring the wind velocity in Titan's atmosphere is difficult. Theoretical wind sp eeds ranging up to 360 km/hour are p ossible, but the image pixel size is 290 km. Results may b e questionable. Method: Detect cloud edges and their motions in a time interval. To increase accuracy, the pixel size must b e reduced by interp olation. The time interval should b e reasonable. If it is too small, then no significant motion will b e detected. If it is too large, on the other hand, clouds may disp erse so much that no corresp onding edges can b e identified. Furthermore, to determine the velocity (including sp eed and direction) at least two crossed edges in each image must b e detected. This is accomplished by image edge detection (enhancement) and morphological processing. Programs: The key programs are: magnify in IRAF for interp olation; and sob el and thin in IDL for detecting edges and then thinning (morphological processing) them, resp ectively. Results: Two groups of CH4 images at 889 nm wavelength, with a time difference of 1.017 hours are processed. The two images within each group are


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combined to improve SNR. The magnification factor is 9, resulting in a (small) pixel size of 31.8 km. Numerous edges were detected, but discounted b ecause of apparent alignment with rows, columns or diagonals. Only one bifurcation p oint detected in each of two groups is considered to b e significant (Figure 4). There is a displacement from B1 to B2 of 7.0 small pixels. The apparent sp eed is 31.8в7.0/1.017 220 km/hour. The direction is -5 3 with resp ect to Titan North. . 5. Dithering

Problem: Low spatial resolution. The pixel size on the CCD chip (PC1 in our case) is large compared with the width of PSF, resulting in "undersampling." Method: Combine images shifted by subpixel amounts. Increasing spatial resolution means reducing the pixel size. We can change the p ointing of the telescop e so that successive images are shifted along each axis by subpixel amounts, say a multiple of 1/2 or 1/3 pixel size, then combine these images to obtain a single image having a smaller pixel size on a finer grid. This technique is called dithering (HST WFPC 2 Handb ook 1995). Programs: The program TinyTim is used to generate PSFs associated with dithered images. These images and PSFs are input to the task acoadd in IRAF/STSDAS to get a single image with improved resolution. Results: Simulation gives good results, but our HST data do not. The reasons include: insufficient p ointing accuracy of the HST, and insufficient SNR in the images. Also, b etter software for dithered image processing may b e needed. 6. Conclusion

Image processing techniques do help to extract information from HST images. MEM and MLM can b e used for deconvolution. The method subtraction and filtering can b e used to detect changes b etween images. More exp eriments using the method edge detection and morphological processing are necessary. For the sophisticated method dithering to succeed, every effort should b e made to achieve the nominal p ointing accuracy of the HST, 3 milliarcseconds. At least two observations must b e made at each p osition to increase SNR and facilitate cosmic ray removal. References Beatty, J. K., & Chaikin, A., eds. 1990, The New Solar System (Cambridge, MA: Sky Publishing Corp.), Chap. 14 Hubble Space Telescop e WFPC2 Instrument Handb ook, v. 3.0, June 1995 Lorenz, R. D., Smith, P. H., & Lemmon, M. T. 1995, BAAS, 27, 1104