[SIP Image]

How to process images with SIP

Digital imaging and image processing form the core of modern astronomy. Much of what we know about the structure and behavior of planets, stars, interstellar clouds, galaxies, exotic objects, and the universe as a whole has been learned from the processing and analysis of images. Your instructor may have specific instructions for how you should process and analyze images using SIP. This page outlines the basic things you can do. There are many ways you can use SIP to work with images. You are not limited to specific tasks since SIP, like a hand calculator, allows you to combine images mathematically, or manipulate one image using standard arithmetic procedures (e.g., addition, subtraction, multiplication, division, raising to a power, mulitplying by constants, adding constants, etc.). In the end, you are limited mainly by your imagination.

In addition to discussion of how you can carry out basic image processing tasks, this page discusses an Example Image Set for Processing and Analysis that is provided at this website. Other sources of FITS images for analysis are

Standard CCD Image Processing Procedures

Digital astronomical images taken in visible light (so-called "optical" images) are taken using a "charge-coupled device" camera, or CCD camera. These camera's have the same imaging chips as are present in many camcorders and personal digital cameras.

Raw CCD images of the sky must be corrected for a number of "errors" produced by the image taking process. Astronomical images downloaded from the web may already have been subjected to these processing procedures, and so one can proceed directly to Further Processing or Image Analysis. This section describes the procedures done to correct raw CCD images for these errors.

Any pixel value in a raw image taken at the telescope is related to the number of electrons collected in that pixel during the exposure. In the ideal the number of electrons is exactly proportional to number of photons from that portion of sky imaged onto that pixel. In practice the number of electrons is equal to the number that were freed by photons from the sky impacting on that pixel and by thermal agitation in the pixel (the "dark current"). Furthermore, the pixel value is typically biased upward from zero by some additive amount, even before the exposure starts. Finally, the number of electrons produced by sky photons is dependent upon the sensitivity of that particular pixel to incident photons (due in part to variations in structure across the chip, and in part to variations in the efficiency of the optical system's delivery of photons to various locations on the chip). The standard procedures used to correct raw images for dark current, bias, and sensitivity variations are described at length in various sources. What follows is a simplified discussion of the steps necessary to implement such procedures using SIP.

Dark current correction. Dark current fills each pixel with electrons at a steady rate dependent upon the temperature of the CCD chip. The final number of electrons contributed by the dark current depends upon the temperature of the chip and the length of the exposure. The standard way to correct for this added error in the pixel values of a sky image is to subtract an image that contains only the dark current contribution to the sky image. The image to subtract is made by taking an exposure of the same length of time as the sky exposure, and with the chip at the same temperature, but with the shutter closed: a so-called "dark image." If you are taking images yourself with your own CCD/telescope system, you will be acquiring a "dark image" image yourself, along with your sky image. Some CCD systems automatically subtract a dark image at the time you take your sky image.

How to correct the sky image for dark current contribution? Simply subtract the dark image from the raw sky image. In SIP this procedure is done using the "Add or Subtract another Image..." selection under the Process menu item.

Bias correction. CCD cameras typically add a bias value to each image they record. If you know that the same specific bias value has been added to each pixel, you can correct for this by subtracting a constant from your sky image. This can be done using the "Add or Subtract another Image..." selection under the Process menu item. These cameras may add the bias value to every image they produced, even those produced by their automatic dark correction procedure. So, you may need to make a bias correction for any image you take with your CCD system.

Some CCD cameras add a different bias value to each pixel. Correcting for this sort of bias in SIP can be done by subtracting a separate dark image (which also has the bias in it) from the sky image.

Flat field correction. This procedure corrects for the variation in sensitivity across the chip. In addition to raw images of celestial objects, dark images, and bias images, the astronomer collects one or more "flat field images" while at the telescope. A flat field image is taken while, for example, pointing the telescope at the sky at dusk (or dawn), or while pointing the telescope at a uniformly illuminated screen. The exposure time is typically quite short. The idea is that any variation in a flat field image records the pixel-to-pixel variation in the sensitivity of the imaging system. Once the raw image of the sky is corrected for any dark current (and bias), a flat field correction can be done. The flat field image may also need a dark correction if it was a long exposure (but typically it might not need such a correction). It may also not need a bias correction, if the pixel values are much larger than the bias value.

A standard flat field correction procedure might be to (1) obtain the average pixel value within the (dark/bias corrected) flat field image (call it a) using SIP's "Compute Statistics in Box" selection under the Analyze menu item, then (2) divide the flat field image (multiplied by 1/a) into the sky image using SIP's "Multiply or Divide by another Image..." selection under the Process menu item.

Further processing

Once again, many additional things can be done. One goal of additional processing might be to increase the quality of the final result. High "quality" is equivalent to high "signal-to-noise ratio." A high signal-to-noise image has very little "snow" (randomly varied noise from one pixel to the next) compared to actual brightness levels in the object of interest --- a galaxy for example.

Averaging (co-adding) images. One way to increase signal-to-noise is to average a set of images of the same object. You may need to first shift some of the images so they are accurately aligned with each other (use the cursor to determine the x,y pixel location of specific star in each image, then use the "Shift Image..." selection under the Process menu item). Then, to produce an average of a set of images, use the "Add..." menu item. For example, if one wants to average 3 images, "Open...." the first image, and add to it the second image. Then, using "Add...", add in the third image. Finally, using "Add..." one last time, set a=0.33333, b=0, and c=0, to mutiply the sum of images 1, 2, and 3 by 1/3. The final result is the average of the three images.

Image Analysis

SIP allows you to determine statistics within user-drawn boxes in an image: mean (average), rms ("root-mean-square deviation from the mean"), sum, median, min, max. You can use these statistics to determine signal- to-noise ratios, compare different regions in the image, etc. You can also plot a histogram of image values for any user-drawn or specified box in the image. These analysis results are available under the Analyze menu item. Of course, the image pixel coordinates and pixel value can be determined by simply moving the cursor to the desired image location. Numerous tasks can be attacked using these simple methods (What is the angular size of an object? What is separation between objects?).

The Process menu item enables further possibilities for image analysis. Let's look at one. If you want to investigate the small scale structure present in an image of an object, a nebula for example, you might consider using unsharp masking. Unsharp masking removes the large scale structure in an image leaving the smaller scale structure. It's a form of "high-pass filtering."

Unsharp Masking. Here is how to do unsharp masking using SIP. First, examine the image you want to process. Unsharp masking can enhance the contrast of smaller features in your image relative to the larger features. What is the typical size of the features you are interested in enhancing? Say it's 5 pixels. Smooth the image with a 5 by 5 smoothing box (use the "Smooth..." selection under Process). Save the smoothed image (either on your disk, or in a storage register). Reload the original image. Select "Add or Subtract another image..." from the Process menu and subtract the smoothed image from the original image. If you want to maintain the same brightness level in the final image as you had in the original, then set a = 3, b= -2, and c = 0. The resulting image is the unsharp masking product. Note how fine scale structure, if present in the original data, is now plainly visible.

Example Image Set for Processing and Analysis

Images http://www.phys.vt.edu/~jhs/SIP/images/m42/m42_1.fit through m42_6.fit are images of the Orion Nebula (M42) taken with an SBIG ST-7 CCD camera on the 0.4m f/4 reflector at the Martin Observatory, Virginia Tech. (For experts: 2x2 binning was used, along with a Bessell R photometric filter.) In each image North is up, East is to the left (approximately). The field of view is approximately 15 arcminutes (East-West) and 10 arcminutes (North-South). The images were taken by students Tripp Cook, Gina Foy, Nathan Smith, and Anubav Vasudevan at Virginia Tech. The date and time of the observation (in the FITS header) are the beginning of the exposure in Universal Time (UT). Each image is a 10 second exposure. These images are supplied so users can try out some of the processing techniques described on this page. These images were automatically dark-corrected at the time they were taken. However, they do need bias correction in SIP (each image has a constant bias of 100 added to each pixel). They will also need flat-field correction, using the flat-field image flat.fit (which is also dark-corrected but not bias-corrected). Following correction, the M42 images can be averaged together (after some shifting) to obtain a final image with a reasonably high signal-to-noise ratio. With specific display parameters it is possible to see either faint nebulosity in the nebula or the 4 central Trapezium stars powering the nebula. Finally, trying an unsharp masking attack on the final image should show some interesting structure within the nebula.
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