DARK CURRENT ELIMINATION IN CHARGED COUPLE DEVICES

Transcription

1 DARK CURRENT ELIMINATION IN CHARGED COUPLE DEVICES L. Kňazovická, J. Švihlík Department o Computing and Control Engineering, ICT Prague Abstract Charged Couple Devices can be ound all around us. They are used in astronomy as a part o telescopes since 80`s o 0 th century. In astronomical images can be ound special type o noise called Dark Current. It`s necessary to remove this type o noise rom images, that s the reason why usage o several basic statistic and iltering method or dark current eliminations have been studied. Applied methods must not damage or remove important objects (stars) in pictures. Results o all used methods are compared rom visual point o view and also by method called Aperture photometry. 1. Introduction Astronomical images are taken with long exposure times, when useul signal on CCDs is generated by photons incident onto photosensitive area. Thermal charge is also generated, in picture is it shown like noise called dark current. Rate o image contamination by noise has a direct proportion to the exposure time. Dark current can be generated in standard conditions like dark room with normal temperature in a ew seconds. Dark current can be described with equation, (1) where A, B are materials constants, T is a temperature in Kelvin and k is a Boltzmann constant (1, J/K). From mathematical point o view, Dark Current can t be describe as random quantity with normal (Gaussian) probability distribution, that s the reason why a lot o methods known or image denoising can t be used or elimination, e.g. thresholding [1]. Table 1: REVIEW OF SOME CHOSEN PARAMETERS OF USED ASTRONOMICAL IMAGE 3m4-d03.sbg.dat Bit Depth 16 Dimensions [px] 1536 x 104 Exposure time [s] 60 CCD`s temperature [ C] 0,19 Ambient temperature [ C] 6,03 Dark current can be removed rom images with method, where more images o same scene is needed. Dark rame is an image, which mapped dark current position in exposed image. It`s made at the same conditions as noisy rame (exposed image with presence o dark current), but objective is closed. Flat ield is a visualization o system optical path telescope ilters - camera. It mapped sensibility o each CCDs pixel on light, vignette and chip impurity. This type o image is made by scan o white area which is lightning uniormly. By dark rame and lat ield is possible to remove dark current rom light rame. Disadvantage o this method is necessity o presence o all 3 types o images. But mostly only noisy or noisy and dark rame are available, so it`s necessary to remove dark current with another methods. All methods have been applied in MATLAB.

2 Figure 1: Astronomical image with Dark current presence. Applied Methods Median ilter belongs to order-statistic ilters used or image noise elimination [, 3]. It`s response is based on replacement o value o the pixel by the median o the gray levels in the neighborhood o that pixel: The original value o the pixel is included in the computation o the median. Median ilter provide excellent noise-reduction abilities with considerably less blurring than linear smoothing ilters o similar size. They are eective in the presence o impulse noise. But median ilter isn`t ilter ideal, because ater its usage some important details can be removed. () Wiener iltering considers images and noise as a random process [, 4]. Target is to ind an estimate o the uncorrupted image. The mean square error between estimate and uncorrupted image is minimized and is given by where is the expected value o the argument. It`s supposed that the noise and the image are uncorrelated, one o the signals has zero mean, and the gray level in the estimate are a linear unction o the levels in the degraded image. Minimum o the error unction in eq. (3) is given in the requency domain by the expression (3)

3 Fˆ v S H ( H vs v vh v S v H ( S 1 H ( H ( H ( S ( / S v / S G v G( ( G( ( (4) where we used the act that the product o a complex quantity with its conjugate is equal to the magnitude o the complex quantity squared. This result is known as the Wiener ilter. The ilter, which consists o the terms inside brackets, also is commonly reerred to as the minimum mean square error ilter or the least square error ilter. The terms in eq. (4) are as ollows: transorm o degradation unction complex conjugate o power spectrum o the noise power spectrum o the undegraded image transorm o the degraded image. The restored image in the spatial domain is given by the inverse Fourier transorm o the requencydomain estimate o. One o the input parameter or this method is noise level o noisy image. This level has been calculated as dierence o power spectrum o noise and undegraded image. Filtering in the Frequency Domain [, 5] is quite simple method and consists o a ew steps: 1. Transormation o noisy image by Discrete Fourier Transorm (DFT) into requency domain, result o this operation is an image spectrum in requency domain F(.. F( is multiplied by a ilter unction H(. 3. Inverse DFT o the result in (.) is computed. H( is called a ilter (or ilter transer unction), because it suppresses certain requencies in the transorm while others leave unchanged. Filtration is made by low-pass ilters, which reduces high requencies, lower requencies are saved. For Dark Current eliminations have been used ilters with rectangle and circle shape. As can be shown on inal images, this method can be used or noise elimination, even though in the background are presented residual ragments o noise. Next think which have to be considered is that i only very low requencies are released, some inormation can be loosed and image can be blurred.

4 3. Perormance evaluation Well-known methods or results examination, like Mean Square Error or Root Mean Square Error aren t appropriate or Dark Current elimination rom astronomical images. To get some objective criterion is used method called Aperture photometry [6]. This method consists in sum o signal source in artiicial aperture. It s quite easy because there is no necessity o usage complicated mathematical procedures and it can be applied on any shape o object. Very important term or this part o work is magnitude. It s photometric quantity used in astronomy which reers to the logarithmic measure o the brightness o an object. This value presents apparent brightness o the star. Value o the magnitude is independent rom real dimensions o the object. Principles o this method can be described in a ew steps: 1. Selection o same object in noisy, noise ree image and image ater application described method. In noise-ree image is reerence object selected. 3. In the others images are ound same objects as in the noise-ree image. 4. Magnitude o reerence object is set to value Comparison o objects magnitudes Method can be considered as successul i magnitude in noise-ree image and image ater some method application are very similar. In Fig. is shown principle o aperture photometry. Figure : Aperture photometry chosen objects rom image cuts, let noisy image, middle noisy ree image with reerence object (Re 1), right image ater Median ilter application 4. Results From visual point o view, median ilter can be considered as very eective method or Dark current elimination (Fig. 3), because rom noisy image have been noise successully removed. All images are shown in inverse visualization or better presentation o results. Result o application Wiener ilter onto noisy picture is shown in Fig. 4. From visual point o view this method can be consider also as successul, even though near stars are presented some ragments which belongs to Dark Current.

5 Figure 3: Result ater median ilter application Figure 4: Result ater Wiener ilter application Results o application Filtering in Frequency Domain are shown in Fig. 5. From visual point o view can be this method classiied either as successul, Dark Current is suppressed, even in the background are visible some ragments which belongs to the noise.

6 Figure 5: Results ater Filtering in Frequency Domain, let rectangle shape o ilter, right circle shape o ilter When results are evaluated by Aperture photometry, it can be said, that successul methods or Dark Current elimination are Median ilter and Filtering in Frequency Domain. Values o object magnitudes in reconstructed images are similar to reerence magnitude. Application o Wiener ilter can t be considering as successul, because magnitude in reerence image is higher than value o reerence magnitude. All results are summarized in Table. Table : COMPARISON OF MAGNITUDES object magnitude Reerence noise-ree image 10,000 Noisy image 9,903 Median ilter 9,954 Wiener ilter 10,43 Filtering in Frequency domain rectangle shape 9,986 Filtering in Frequency domain circle shape 9, Conclusion The dierent methods or Dark Current eliminations rom astronomical images have been studied in this work. Dark Current is a noise which can t be assumed as Gaussian, so there is no possibility to use e.g. thresholding or image denoising. From visual point o view shows all applied methods as successul, all methods prove ability to remove this kind o noise. Evaluation by Aperture photometry gives us little bit dierent results. Median ilter and Filtering in Frequency Domain we can consider also as successul, because by magnitude comparison we obtain quite similar values. But value o magnitude obtain ater application o Wiener ilter is higher than reerence magnitude, so this method can t be consider as successul. 6. Reerences [1] Pizurica, A., Image Denoising Using Wavelets and Spatial Context Modeling, Universiteit GENT, 00 [] Gonzalez, R. C.; Woods, R. E. Digital Image Processing, nd edition; Prentice-Hall: Upper Saddle River, New Jersey 07458, 00, ISBN

7 [3] Štork, M., Mediánové iltry a jejich použití při iltraci impulsních šumů, [4] Uhlíř, J., Sovka, P., Číslicové zpracování signálů,. vydání, vydavatelství ČVUT, Praha 00, ISBN [5] January 010 [6] Romanishin, W., An Introduction to Astronomical Photometry Using CCDs, University o Oklahoma, October 006, Acknowledge This report has been made by support o research study MSM Lenka Kňazovická Department o Computing and Control Engineering, ICT Prague, Lenka.Knazovicka@vscht.cz Jan Švihlík Department o Computing and Control Engineering, ICT Prague, Jan.Svihlik@vscht.cz