Practical Translation Rotation and Scaling

The bulk of practical applications, such as image registration, require three transforms translation, rotation, and scaling. Although this could be accomplished as three sequential operations, it is more practical to combine the three transforms into one algorithm. Most important for practical image processing is that the procedure must account for the fact that in many CCDs the pixel dimensions are not the same in the two axes. This is not a problem for translation because all positions in...

Measuring CCD Performance

In this chapter, you will learn two methods for assessing the performance of your CCD camera. The first basic CCD testing is so simple that you can make the necessary observations in a few minutes during the course of your normal observing program, and the second method advanced CCD testing yields a complete performance profile on your CCD. Five characteristics define the performance of a healthy CCD camera the conversion factor, or gain Basic CCD testing checks only the first two items the...

Calibration Frames

As astronomers, we want to know the photon flux that is, the rate at which photons fall on our CCD. Yet a raw CCD image contains the signal we want mingled with a bias voltage, a dark current, and nonuniform photosite sensitivity. To recover the photon flux, we take additional images that allow us to subtract the additive values and divide out the multiplicative factors. These additional images support frames include dark frames, flat-field frames, and bias frames. Support frames provide a...

Recognizing and Correcting Equipment Problems

All images suffer from a certain number of residual defects streaks, black blobs, dark corners the sorts of things that flat-fielding is supposed to eliminate, but does not always remove entirely. On astrophotographs, the same defects are often present, but they are small and hard to see. Because we inspect digital images so closely and apply powerful image-processing routines to enhance contrast, these same defects stand out with great clarity. Common types of image defects are hot spots,...

Angular Field of View of a Detector

The detector occupies an angle at the focus of a lens or telescope called the angular field of view. Recall that the image of an object is formed at a height h from the optical axis where F is the focal length of the telescope and ft is the angular distance from the optical axis. Assuming that the center of the detector, with a dimension det, is placed on the optical axis of the telescope, then ddet 2h , and a detector captures a field of view ftfov ftfov 2arctan ) radians (Equ.1.17) for a...

Auxiliary Optics

Telescopes generally have a fixed focal length, but for your imaging projects, you may want to have more or less sky coverage, or to increase the resolution (sampling) of the optical system, or you may need to correct an aberration such as coma in the optics of the telescope. These goals are often accomplished through the use of some kind of auxiliary optics placed in the optical train between the telescope and the camera. A focal reducer is a positive (i.e., converging) optical assembly that...

Basic CCD Testing

To be practical, CCD tests must be simple enough to be carried out without fancy test equipment. You can do basic testing without even taking your CCD off the telescope This consists of shooting two bias frames, two flat-field frames, and one dark frame. That's it. The analysis takes about five minutes. Details are given in Section 8.2.1. Advanced CCD testing is more complex. It requires building a low-level light source (L3S), and with it shooting nine bias frames, nine low-level flat-field...

Processing Color Images

Digital cameras, webcams, and Bayer-matrix astronomical CCD cameras capture color images directly, and after scanning, negatives and photographic prints provide a further source of images that can almost certainly benefit from digital image processing. In this chapter, we examine what to expect in digital color images, how to collect good color images, and how to process color images Unlike CCD cameras, digital cameras deliver a color image to you as a complete package. With CCD cameras, a...

Practical Astrometry

In the preceding sections, we have seen that astrometry is a four-step process first measuring (jc, y) locations for each reference star and collecting the corresponding right ascensions and declinations second, computing plate constants for the image third, measuring the (x, y) positions of target objects and last, computing the coordinates of the target objects. Software makes the computationally intensive second and fourth steps nearly invisible to the user, making good astrometry a two-step...

Determining a Centroid

The centroid of a physical object is its barycenter, or center of gravity. It is the point at which the object suspended from a thread or teetering on a fulcrum-balances. In an image, the centroid is the point at which the values of all surrounding pixels are balanced. What makes the centroid interesting is that even though light from a star is spread over many pixels, the distribution of light among them enables us to recover the exact center of the star image within a small fraction of a...

Image Ranking

Rank operations among sets of images provide ways to find extreme values and also to eliminate extreme values. The most useful rank operation is the median, which finds the pixel value for which an equal number of images have a lower pixel value and a higher pixel value. The resulting median image will be free of abnormal pixel values caused by cosmic ray hits and local electronic noise. Although the minimum and maximum image operations have rather limited and specialized uses, they are...

The Calibrated Image

Raw Darkness Trial

The calibrated image should be an accurate, albeit sampled and quantized, copy of a section of night sky. In the ideal image, pixel values are directly proportional to the average flux of photons falling on the CCD during the integration. The most amazing thing since we don't live in an ideal world is that real-world calibrated CCD images really do approach the ideal. Observers using rather ordinary small telescopes routinely reach 20th magnitude, and routinely pull down images good enough to...

JPEG File Compression for the Internet

The Joint Photographic Experts Group is a standards organization that defined the method of data compression used in JPEG files, technically known as the JPEG File Interchange Format (JFIF), and informally as JIF or JPG. The JPEG data compression method is sometimes used in TIFF files, as well as other popular file formats. JPEG exists to enable users to store and transmit 24-bit color images in significantly fewer bytes than a straight bitmap image would require. JPEG is a lossy compression...

Non Linear Operators

The previous chapter described neighborhood processes using linear operators. This chapter explores the properties of non-linear operators. These powerful and sometimes perplexing processes are extremely useful in astronomy. Unlike linear operators, non-linear processes usually include a logical if then operation. Because these built-in conditions can cause abrupt discontinuities, the output values cannot be traced back to unique input values. The distinguishing feature of conditional operators...

Info

Data for Cookbook 245, 378-wide External Binning, Low-Dark-Current Mode lines (relatively low frequency). If a pattern is present, it may vary randomly from line to line, or it may be fixed from one frame to the next. Patterns may originate inside the camera or may be interference from a nearby computer or monitor. Note whether the pattern is the same from one frame to the next (and therefore generated in the CCD electronics), or whether it changes from frame to frame (and therefore comes from...

C76 Wavelet Spatial Filtering

One of the most exciting image processing technologies to come along in recent years is wavelet processing. AIP4Wiri s Wavelet Spatial Filter provides unique capabilities for image enhancement not matched by other processing techniques. To get the most out of this tutorial it is recommended that you read Chapter 18, so you will have a better idea of what is happening, as well as a better understanding of the terminology. For this tutorial, be sure that Auto Lo HiStretch is selected as the...

O

From the raw image, where Q (read as Q-bar) is the average quantum efficiency of the CCD array. Preparation for calibration consists of the following steps 1. Averaging or taking the median of the dark frames to create a master dark frame. Note that the integration time used for the dark frames must be the same as the integration used for the raw images. 2. Averaging or taking the median of the raw flat-field frames to create a combined raw flat-field frame. 3. Averaging or taking the median of...

Second Edition

Box 35025 Richmond, VA 23235 Toll Free 1 (800) 825-7827 (804) 320-7016 Fax (804) 272-5920 Published by Willmann-Bell, Inc. P.O. Box 35025, Richmond, VA 23235 Copyright 2000-2005 by Richard Berry and James Burnell Second English Edition All rights reserved. Except for brief passages quoted in a review, no part of this may be reproduced by any mechanical, photographic, or electronic process, nor may it be stored in any information retrieval system, transmitted, or otherwise copied for public...

Shooting Calibration Frames

Calibration plays an integral role in making top-notch CCD images but in the excitement of imaging faint nebulae, changing filters, or battling intermittent clouds, it is tempting to skimp on shooting calibration frames. Unfortunately, skimping on calibration steals away the very qualities you want most in your celestial imagery. We discussed the basic idea behind accurate photon counting in Chapter 2, and cover calibration in full detail in Chapter 6. In this section, we focus on the practical...

Van Cittert Image Estimation

Van Cittert deconvolution is one of the simplest and most robust methods of iterative image estimation. It was proposed by P.H. van Cittert in a 1931 paper on the influence of scattered light on the intensity distribution of spectral lines, and has been independently discovered and improved since, particularly by Landweber and Bialy, who often receive credit for a more general description of iterative image restoration than van Cittert's original paper. Figure 19.5 At a larger image scale, the...

Translation

Translation means shifting an image up, down, or from side to side. The image itself is not changed, but simply moved to a new location. Each pixel P(x, y) becomes a new pixel P(x', ). The equations for translating a point are where x and y' are the coordinates of P in the new image, x and y are the coordinates in the old image, and xT and yT are the shifts in the two axes. There are many reasons for wanting to employ translation, but the most common application is to register one image...

C13 Color Images

This tutorial demonstrates the basic color operations of AIP4Win. The files used in it may be found in the Color subdirectory of the Tutorial directory on the CD-ROM. The files comprise a calibrated RGB image set of the Eagle Nebula, Ml6, taken by Neil McMickle of Stanhope, New Jersey, using a MX716 CCD camera and a set of RGB dichroic filters and an IR-blocking filter through a 4-inch fluorite apochromatic refractor. In this tutorial we will register four individual filtered exposures and...

B

Where G, B is the original color triad, R G E is the adjusted color triad, and the coefficients of the transform matrix are ctj. A matrix multiplication takes place in your digital camera every time you make a picture. If the values of the matrix coefficients cu, c22 , and c33 are set to 1.0, and all other ctj s are set to zero, the new triad comes out identical to the original triad. But if cu is greater than 1.0, the new image will be redder. The coefficient c22 controls green, and c33...

T

Figure 13.10 Logarithmic scaling increases the lowest pixel values so strongly that the sky background often becomes overly bright. By mixing the logarithm with a linear scaling, logarithmic scaling can produce strong enhancement without loss of detail in the brightest parts of an image. is cancelled, so that the light output on the monitor is directly proportional to the numerical values in the image. Tip In AIP4Win, you set the monitor gamma using the Image Display control. 13.2.2.3 The...

Overview of FITS

FITS is simply a standardized way to store image data. By design, FITS is friendly to both humans and computers, meaning that you can peek into FITS files with a text editor and figure out what's going on. However, the very flexibility of FITS since it can also store data tables, multiple groups of data, multispectral images, and arrays with up to 999 axes has almost become its undoing. No all-purpose software can cope with the range of valid non-image FITS files. When Wells, Greisen, and...

Optics for Imaging

Choosing the best telescope for digital imaging is worth an entire book, but the basics can be summarized in a few paragraphs. For any type of imaging, the choice of telescope is a trade-off among the desired field of view, the desired resolution, and the desired length of exposures. For a given aperture, a short focal length means a wide field of view and shorter exposures (or more data in same-length exposures) at some cost in resolution. Longer focal lengths mean more resolution, but a...

Properties of Color Images

Random Pixel Pattern

Digital cameras, DSLRs, and webcams perform remarkably well in astronomical applications. However, it is important to remember that these cameras were engineered for short-exposure daytime terrestrial imaging rather than low-light long- exposure astronomical imaging. It is therefore hardly surprising that the cameras and their file formats are optimized for daytime picture-taking rather than for astronomy. With proper attention to technique, however, you can make excellent astronomical images...

Aspect Ratio

To reconstruct the image sampled by the sensor, it is necessary to know how the mass of bytes is organized. This topic is treated fully in Chapter 3. This information is usually conveyed from the electronic camera to the computer in a file header. When a computer program opens an image, it begins by reading the header. The image can then be reconstructed on a computer monitor in the pattern of columns and rows matching that of the photosites. If this is done correctly, the computer screen will...

Raw Nef and CRW Proprietary Raw Images

Most digital camera owners prefer the convenience of getting a finished JPEG image from their camera. However, a few oddball types such as amateur astronomers want to extract every scrap of information from the sensor and for them, Nikon, Canon, and other high-end digital camera makers allow users to dump unprocessed output from the CCD or CMOS directly into a file for later analysis and processing. Unfortunately, the data format of these proprietary files is either entirely undocumented or...

Deconvolution

Deconvolution attempts to restore an image that has been degraded to its original pre-degraded condition. Image degradation stems from two sources convolution of the image before detection, and noise added to the image in the process of detection. Atmospheric turbulence, telescope optics, and mechanical instability account for pre-detection convolution. As parallel rays of light from a distant star pass through Earth's layered and inhomogenous atmosphere, they are refracted in slightly...

Convolution in One Dimension

In convolution, two functions are overlaid and multiplied by one another. One of the functions is an image and the other is a convolution kernel that is, one function is represented by a large array and the other by a relatively small array. In convolution, the kernel operates on the image which is why it is called an operator. Consider a one-dimensional section extracted from a sharp image These pixel values might be a slice from any abrupt change in brightness in an image, such as the edge of...

Angular Size of a Single Pixel

The equations for calculating the angular size of a photosite on the CCD and the corresponding pixel in the image are the same as those in the preceding section although, of course, the pixel angles are much smaller. We continue the example above, noting that the photosites on the CCD are 17 microns wide by 19.75 microns high. Set up the equation as follows fov 2 arctan Q Q()q) tradians (Equ.1.20) If you carry out the second calculation, you will discover that the pixels are 3.5 arcseconds wide...

TIFF The Standard in the Graphic Arts

TIFF is the image file format preferred in the graphic arts industry. Photo-editing software, paint programs, and desktop-publishing applications use TIFF because it is a powerful and flexible image format. However, this very flexibility is sometimes the undoing of TIFF. This standard supports black-and-white binary images, 8-bit grayscale images, 8-bit palette color images, 16-bit RGB color images, 24bit RGB color images, as well as specialized graphics needs such as 32-bit CMYK color. TIFF...

C51 Single Star Photometry

From the Photometry subdirectory under the Tutorials directory, load and display the image M82-x20.fts. If you view the FITS header for this image, you will see that it is a stack of twenty 60-second exposures of the galaxy M 82. Step 1 Open the Single-Star Photometry Tool. Open the Single-Star Photometry Tool by clicking the Measure I Photometry I Single Star menu item. On the Settings tab, you will see three sets of text boxes and up down controls for setting the star aperture and the inner...

I

*From Bessell, UBV(RI) Filters for CCD Photometry, CCD Astronomy, Vol. 2, No. 4, p. 21. magnitudes magnitudes measured with light between 495 nm and 580 nm wavelength. The availability of photographic and photo visual magnitudes opened new areas of research. Suddenly astronomers had a way to measure the temperature of stars from their color index from the difference between their photographic and photo visual magnitudes. The color index correlates well with the surface temperatures of stars and...

Goals in CCD Testing

The primary goal of characterizing your CCD camera's performance is to verify that it is operating correctly. Once you have established that the noise level is at or better than specification, your goal in testing will be to check its performance from time to time, to be sure that nothing has changed or degraded. In this way you can rest assured that your CCD camera is in tip-top shape. When should you test your CCD Wait until the thrill of shooting your first images wears off, when you have...

Image Registration

Astronomers often compare images taken at different times to search for comets, asteroids, variable stars, optical gamma-ray bursts, and supernovae. They also combine images to improve the signal-to-noise ratio over what they can obtain in a single integration, or to composite images into mosaics or color images. However, because telescope pointing is never exactly the same in two images, they must be brought into coincidence, or registered, before the images can be compared. Registration thus...

C74 Unsharp Masking

Unsharp masking is a powerful technique for exposing detail in an image where bright regions tend to wash it out. It is especially useful with planetary images, bright nebulae and overexposed galaxy cores. It is the real workhorse of the planetary imager. For this tutorial, be sure that Auto Lo H Stretch is selected as the default display mode in the Image Display Control window. Step 1 Load an Image. From the Image Enhancement Tutorial subdirectory, load 03119204.ccd. This is a nice clean...

C11 Deep Sky Images

Up to this point, the tutorials have been focussed on specific features of AIP4Win. This and the following tutorial demonstrate using a group of AIP4Win functions to solve typical image processing challenges. This tutorial focuses on enhancing deep-sky images. The task to be performed in this tutorial is the calibration and enhancement of a typical track-and-stacked deep-sky image. Images of this type share a number of common characteristics. Since they are images of faint objects, they are...

Exploring Frequency Space

The fundamental idea behind frequency-domain image processing is that every image can be decomposed into a unique spectrum of spatial frequencies. We can apply this concept by altering the spectrum and then transforming it back to a new image that has changed characteristics. With appropriate alterations to the spectrum, we can enhance image detail, alter the energy distribution in the image, and remove noise just to name a few of the many applications. When we speak of frequency, we normally...

01 photon

Figure 2.2 The greater the number of photons, the better the signal-to-noise ratio. In this case study, the photon count across the face of the galaxy image varies from a mean value of 0.1 photons to a mean value of 10,000 photons. The signal-to-noise ratio equals the square root of the photon count.

Signals and Noise in Images

Dark Current Noise

You now have enough background to examine the signals and noise that you will encounter in real images from your CCD or digital camera. Before beginning that examination, we need to get certain units of measurement squared away. We introduced signals and noise in terms of detected photons, electrons, and ADUs that is, in different units. To understand digital images, it is necessary to know how these different units relate to one another. When photons strike a detector, not all of them generate...

Aip

Figure 16.3 Multiplication can produce a wide range of results. In this example, the pixel value of the black background is zero, while that of the white lettered areas is 1.0. When the Horsehead is multiplied by the letter image, background areas become zero while the lettered areas retain their original values. In image processing using integer pixel values, multiplication must be normalized to produce results in the range of values found in the images. However, with floating-point pixel...

Linearity Saturation and Blooming

Astronomers prize CCDs for their linear response to light, that is, the output signal is directly proportional to the number of photons that fell on each photosite during an exposure. When the number of photoelectrons accumulating during an exposure reaches the holding capacity of the charge well, the photosite is said to be saturated. Ideally, when a CCD reaches saturation, it would cease responding to further photons. Unfortunately, that does not happen. Bright stars in the CCD field of view...

Sampling the Image

Detectors do not reproduce images in toto, but rather, they sample the image. This means that the image is broken into discrete small chunks. With electronic sensors these are called picture elements, or pixels. The pixel structure dictates the smallest features that will be visible in a digital image. Electronic sensors sample images in a very simple way photons that fall on a photosite are lumped together as a single pixel value in the image. The CCD thus samples the image at the focus of the...

B45 Photometry Software

Unified Software Systems, PO Box 23875, Flagstaff, AZ 860023875. (520) 774-8629. (Prop Arne Henden) Software for reducing CCD and photoelectric photometry. Info http www.flagstaff.az.us -ccdir This site also contains lots of useful information about CCD photometry. EZPhot. Automated CCD photometry reduction software. Available on the Web as shareware. Info http www.mtco.com jgunn. H& K. Also called Software for Photometric Astronomy, Arne Hendon and Ronadl Kaitchuck, Willmann-Bell,...

Pixel Count

Given the pixel count and the physical width of the detector, you can find the pixel size by dividing the detector width by the pixel count To find the width of the photosites in a webcam with a 4 x 3 mm detector listed as having 640 x 480 pixels, divide 4 mm by 640 pixels pixel 0.00625 millimeter , (Equ. 1.15) or 6.25 microns. The same holds true for the pixel height, and in this case, the pixels are 6.25 microns square. Given the detector size and pixel size, you can find the pixel count. For...

The Image Histogram

A histogram is an inventory of the pixel values found in an image. It is a graph that plots the number of pixels of each pixel value on the y axis versus pixel value on the x axis. Although a histogram contains no explicit information about the image contents, the distribution of pixel values implies a great deal about the image. Because of the enormous range of brightness captured in astronomical images, the histogram is usually plotted as the logarithm of the number of pixels versus pixel...

Matching Pixels to the Point Spread Function

The point-spread function of a telescope (ideally, the Airy disk) defines a characteristic dimension for the smallest details in a telescope image. To reproduce all of the detail present in the image, the sample size must be small enough to define the bright central core of the diffraction disk reliably. The Nyquist sampling theorem in communication theory states that in sampling a wave, the sampling frequency must be two times the highest frequency present in the original. Music recorded on...

C93 Multi Image Alignment

You can also choose to align a set of images without stacking them. This is provided so that you can combine the images using the Movie Tool into an AVI movie that can be played back on any PC running Windows. Several movies have been provided on the CD-ROM that have been created using this technique. Multi-Image Alignment is performed when you select Individual Files for the Process Type and select 1 Star or 2 Star Alignment and select a Master Frame. Other than that, it is identical to...

Color Imaging with CMY Filters

Imaging with CMY (cyan, magenta, and yellow) filters is an interesting variation on imaging with red, green, and blue filters. The techniques share much of their methodology because CMY filters are closely related to RGB ones. Each filter in a CMY set combines two passbands from the RGB set. These combination passbands are The important point is that after taking images through CMY filters, it is possible at least in principle to recover red, green, and blue signals that can be used to create a...

C75 Deconvolution

Deconvolution as a technique for restoring astronomical images became really 650 Handbook of Astronomical Image Processing well known when it was discovered that the Hubble Space Telescope mirror was flawed. The near miraculous ability of this computationally intensive technique saved the day for NASA, and, judiciously applied, can be used to reduce the effects of atmospheric seeing and slightly less-than-perfect focus in your own images. In this tutorial we will use the two types of...

The Topographic Operator

This operator treats the pixel values in an astronomical image as elevation in a digital terrain map, to create a shaded relief image. The resulting bas-relief produces a more realistic illusion of a three-dimensional surface than the simple bas-relief kernel described in the previous chapter, because the new pixel value is based on the behavior of diffusely reflecting surfaces. What the topographic operator does is to figure out how the image would look if it were sculpted as a relief in...

When you are finished close all the open images C73 Convolution Filtering

Convolution filters are rather coarse devices used to sharpen or soften an image. You can use them on lunar and planetary images to help remove the softness caused by poor focus and bad seeing. You can also use them to build your own unsharp masks, although AIP4Win provides several ways to do this automatically. Essentially, these filters are useful building blocks of more complex operations. For this tutorial, be sure that Auto Lo HiStretch is selected as the default display mode in the Image...

Richardson Lucy Image Estimation

The Richardson-Lucy iteration was described by William H. Richardson in a 1972 paper on iterative methods of image restoration, and two years later by L.B. Lucy in a paper in the Astronomical Journal. This method is usually called the Richardson-Lucy method, but in the literature on deconvolution you will also find it called the Lucy-Richardson method, the RL method, the expectation maximization method, and the method of maximum likelihood. The van Cittert method is based on an additive...

Morphological Operators

Isophotes Photoshop

Morphology deals with form and shape in image processing, morphological operators are tools that aid the observer in defining, extracting, and manipulating the Figure 15.9 Isophote contour lines encircle a region having pixel values greater than the isophote pixel value. This highly enlarged section of the M101 image shows a knot in the spiral arm, an isophote contour line drawn around that knot, and the same isophote line superimposed on the image. Figure 15.9 Isophote contour lines encircle a...

Distance on a CCD Image

The distance between two points on a CCD image is the very simplest form of as-trometry, the science of measuring the positions of heavenly bodies. The points can be integer pixel positions or the non-integer centroids of star images. The distance d between two points on the surface of a CCD is d *j xx-x2)2 + (yx-y2)2 (Equ.7.12) where (xv jj) and (x2, y2) represent the two locations. The x-axis is conventionally taken as the sample direction, and the y-axis as the line direction on the CCD. On...

B67 Image Processing Software

By James Burnell and Richard Berry. Windows PC-based. Your copy of AIP4Win 2.0 is included on the CD-ROM bound into this book. AIP4Win 2.0 is a versatile and powerful package of software tools for calibrating, analyzing, enhancing, compositing, and saving monochromatic and color images from CCD cameras, scanned astrophotography, and the Internet. Updates available to registered users. Info Astroart. By Marino Nicolini. Windows PC-compatible processor required features a wide range...

Photometry

Astronomers refer to the determination of a celestial object's brightness as photometry. Even though a star image may sprawl over many pixels, because CCDs are linear, they accurately record the total amount of light in each pixel, and therefore, also record the total light in any feature. Star images present something of a problem, however, because the starlight is mixed with light from the background sky. Extracting an accurate measurement of the total light in a star image is tricky, but it...

Magnitudes How Bright Is This Star

Aperture Photometry Freeware

The ancient Greeks divided stars into six classes by magnitude, literally by their size. Between 141 and 127 B.C., the Greek astronomer Hipparchus compiled a catalog of about one thousand naked-eye stars, listing both positions and magnitudes. Just as we do today, this catalog listed the brightest stars as first magnitude, and the faintest visible to the naked eye as sixth magnitude. Nearly two thousand years later, the English astronomer Norman Pogson quantified measures of star brightness,...

Wavelet KSigma Filtering

Light Noise Texture

In the section above, we saw that wavelet filtering can remove noise from images providing it is well-behaved Gaussian noise. However, CCD and digital camera images usually contain a mixture of Poisson noise, Gaussian noise, and complex noise types generated in dark subtraction, flat-fielding, and image stack- Figure 18.11 Wavelet kCS filtering filters images with any noise type, but requires that the user specify the acceptable noise level at each wavelet scale. In this example, a standardized...

Y y yt

Finally, to insure that the program does not attempt to access the old () array outside its bounds, you must check that both x and y lie within the bounds of old (), and if they do not, you must assign a value to new (), in this case zero. Recall that the array dimensions run from 0 to xmax and 0 to ymax. FOR yp 0 to ymax FOR xp 0 TO xmax x xp - xt y yp - yt IF x< 0 OR x> xmax OR y< 0 OR y> ymax THEN new(xp,yp) old(x,y) END IF NEXT xp NEXT yp Thus far we have assumed that you can get...

Calibrating Images

Image Processing Subtraction

In an earlier chapter, we detailed the theory of image calibration. This section treats calibration as an image operation, as indeed it is. The first two subsections deal with dark subtraction and flat-fielding, and the following three examine the operations used to apply the basic, standard, and advanced calibration protocols. CCD images consist of multiple layers of signal and noise. The simplest raw image type is a bias frame, an integration of zero duration made in total darkness. Bias...

Spectra and Spectrographs

Spectroscopy requires separating light of different wavelengths yet in a telescope, (theoretically at least) light of all wavelengths comes to focus at the same point. Spectroscopy, therefore, requires an auxiliary optical element or instrument to disperse the light so that different wavelengths fall on different places on the detector. Such instruments are called spectroscopes when used visually and spectrographs when the spectrum is recorded on photographic film or with an electronic camera....

The Wavelet Transform

Wavelet Image Processing

The most efficient way to compute the wavelet transform is to use a function like Figure 18.1 Five wavelet scales reveal different spatial structures in the classic Lena image. Scale 1 shows small spatial structures with a kernel radius of 1 the radius of the Scale 2 is 2, that of Scale 3 is 4, and so on each wavelet scale doubling the radius of the preceding scale and showing large structures. Figure 18.1 Five wavelet scales reveal different spatial structures in the classic Lena image. Scale...

Richards Remarks

Nine years have passed since Introduction to Astronomical Image Processing, the forerunner of this book, appeared. In its preface, I wrote Back in 1965, Mariner 4 sent the first close-up pictures of Mars back to Earth. I was a teenager, and terrifically impressed that pictures could be radioed to Earth from a planet millions of miles away. And, despite the fact that Mariner 4's camera didn't work quite right, over a period of months, scientists at the Jet Propulsion Laboratory discovered that...

Deep Sky Imaging

For the most part, when amateurs think about CCD imaging, their goal is to image faint, fuzzy, deep-sky objects. (Operationally, the deep-sky list ought to include comets as well as nebulae and galaxies because comet are just another type of faint, extended object.) Astronomical CCD cameras are phenomenally successful at imaging deep-sky objects for three reasons (1) their high quantum efficiency, (2) their linear response to low-level light, and (3) the ease with which you can correct their...

C72 Histogram Shaping

The previous tool, Brightness Scaling, operates on an image by examining the range of pixels in it and assigning new pixel values based on where each lies in the range between the values selected for black and white. Histogram Shaping, while looking superficially similar, works in an entirely different way. While both tools reassign each pixel value in the original image to a new value, Histogram Shaping does it by trying to force the histogram of the image, as a whole, to a new shape. While we...

C8 Fast Fourier Transform

AIP4Win implements one of the most powerful of all image processing tools spatial filtering. The Fast Fourier Transform (FFT), the basic process behind most spatial processing, is covered in Chapter 17. Before running this tutorial, read this chapter to gain an understanding of spatial filtering. The Fast Fourier Transform is a computationally accelerated technique for determining the frequency spectrum of a signal. In two dimensions, it can be applied to an image. The reason for transforming...

Histogram Specification

Histogram specification takes the process of specifying the desired characteristics for the new image a step further than histogram endpoint specification the user specifies the histogram of the new image. A scaling algorithm then computes the transfer function necessary to reshape the histogram of the original image into the desired histogram for the new image regardless of the shape of the original one. The user does not need to know anything about the old histogram it is necessary only to...

Photometric Observing

This section sketches the practical side of the three basic types of CCD photometry all-sky, do-what-you-can, and differential. Use the method that is most appropriate for your circumstances. The goal of differential photometry is to produce accurate magnitude differences between (supposedly) steady comparison stars and program stars. Differential photometry asks, How has this star changed Not surprisingly, this technique is much easier than all-sky photometry because, to a first approximation,...

Remapping Pixel Values

After an image is calibrated, the pixel values in the image are directly proportional lo the amount of light that fell on the CCD. In the case of scanned photographs, Figure 13.3 In this image, a low endpoint of 0.10 allows the lowest-valued 10 of the pixels to saturate black. To show where information has been lost, black-saturated pixels are printed white. Because these pixels represent sky, their loss may pass unnoticed but the information they once contained is gone. Figure 13.3 In this...

C2 Calibration

This tutorial demonstrates how to use A P4Win to calibrate CCD images. The supporting images for it are contained in the Calibration subdirectory of the Tutorials directory on the CD-ROM. A frame produced by a CCD camera contains a lot more than an impression of the light that fell on it. As described in Chapter 6, the frame also contains noise and artifacts. Using AIP4Win's calibration tools we can remove most of this noise and generate an image with scientifically useful information, which is...

Astrometric Theory

Projection Ccd

Astrometric accuracy depends on having a precise reference frame within which the position of celestial objects can be measured. Using a typical amateur's telescope equipped with a CCD camera, observers routinely make measurements to a precision of 0.2 arcsecond or better. The key concept is that astrometry measures the relative location of a star in an image that covers only a small section of the sky with a precision of 1 part in 5,000 relative to a background of stars whose positions are...

Blinking Images

Blinking gets its name from the blink microscope, a tool that astronomers use to compare photographic plates. In this instrument, relay optics allow the observer to view two photographic plates simultaneously at low magnification. Each plate is lit by a lamp with both lamps turned on, the observer moves the two plates until the images coincide. By alternating which lamp is turned on, the observer's view switches between the two plates. Where none of the stars has changed, the two plates look...

C10 Image Registration and Blinking

In this tutorial you will learn how to align two images into accurate sub-pixel registration and then blink them to search for asteroids. The image files can be found in the Image Registration subdirectory of the Tutorial directory on the CD-ROM. We used one of these files earlier in the As-trometry tutorial (Section C.4). They consist of a pair of images, taken just 26 minutes apart, of a trio of asteroids. We will use the Register Images Tool to align one image with the other then we will use...

C53 Multiple Image Photometry

Though the Single-Image Photometry Tool provides a fast and accurate means of measuring stellar magnitudes, the real power of a computer comes into play when you have a series of images taken over time of a variable star and want to automatically extract the brightness data to create a brightness curve. AIP4Win provides this capability via the Multiple Image Photometry Tool. For this tutorial, unlike the others, the images can be found in the Sullivan subdirectory of the Images directory on the...

Limited Warranty Statement

Authors warrant only to You that the Software shall perform substantially in accordance with accompanying documentation under normal use for a period of NINETY 90 DAYS from the purchase date. The entire and exclusive liability and remedy for breach of this Limited Warranty shall be, at Author's option, either i return of the list price of the Software, or ii replacement of defective Software and or documentation provided the Software and or documentation is returned to...

FITS The Standard Format in Astronomy

FITS stands for Flexible Image Transport System. It evolved in the early 1980s when astronomers at Kitt Peak National Observatory and the National Radio Astronomy Observatory NRAO began to cope with digital images from the Very Large radio telescope Array and digital images from CCD cameras that were then just coming into use. There had to be some way some standard way to move data from one observatory to another. In response, Don Wells, then at Kitt Peak Eric Greisen at the NRAO and Ron Harten...

Practical RGB and LRGB Color Imaging

Galaxy Filtered Unfiltered

Good RGB and LRGB imaging differ little from monochrome imaging. The defining difference is, of course, that you must shoot the components for color images through color filters. In the early days of CCD imaging, tricolor images were made through gelatin or dyed-glass filters. The classic choices for tricolor imaging were Kodak Wratten filters. Today new high-transmittance interference filters are the best bet for CCD imagers. Wratten Tricolor Filters. Despite their low transmittances, classic...

Generated Kernels for Unsharp Masking

Sharp Point Unsharp Point

The kernels discussed above tend to have small dimensions, but they can easily be made as large as needed. Large kernels are used to enhance the medium-scale spatial features that 3x3, 5x5, and 7x7 ones scarcely touch. Because of their separability, large kernels can be synthesized by performing successive passes with appropriate one-dimensional kernels. Furthermore, the one-dimensional kernels can be generated algorithmically, to match the size and shape of the particular feature or features...

Telescope Mountings

The accuracy of your telescope's clock drive has a profound effect on how you shoot images with a CCD camera. The longer you integrate, the deeper your images. However, background sky brightness, blooming of bright stars, dark current in the CCD, those pesky hot pixels, and most importantly the accuracy of the telescope's drive limit the length of integrations. Unfortunately for CCD users, digital imaging requires tracking about 60 times more accurate than is needed for satisfactory performance...

Image Math

Image math includes adding, subtracting, multiplying, and dividing the pixels in two or more images. These operations are carried out between pixels at corresponding jt,y locations in the images. The resulting pixel value can be placed into anew image array, or it can replace the values in one of the original images. For clarity in the following sections, results are always placed in a new image. Image addition means adding the pixel values in two or more images. N x,y 0l x,y 02 x,y Equ. 16.1...

Jj

Vertical Scale Type Linear Logarithmic Figure C.8 By analyzing the starlight disbursed into wavelengths by a prism or diffraction grating, astronomers can tell the temperature and composition of distant stars. Seen here, the Spectroscopy tool is converting an enigmatic smear of light into a graph displaying the characteristic pattern of hydrogen atoms. fully calibrated standard stars to measure stellar magnitudes. This tutorial demonstrates how to use AIP4Win to extract the spectral curve from...

Fourier Theory

The mathematical theory that Fourier introduced in 1822 was a long way from modern digital image processing. In this section, we examine the four steps that lead from his original series summation to the fast Fourier transform used in image processing the Fourier series, the Fourier integral, the discrete Fourier series, and the fast Fourier transform. Our goal is not to teach you the math, but to show the chain of reasoning that underlies the Fourier transform. 17.2.1 Periodic Functions The...

Preface to the First Edition Acknowledgments

We have used A P4Win to process images during the program's whole development cycle. We have processed thousands of images, tested routines over and over, carried out astrometry, photometry, spectroscopy, shaped countless histograms, blinked for supernovae, and made CCD movies. All of the images in the book were prepared using AIP4Win. But we could not have done it alone. We wish to acknowledge the generous help of many friends and associates. Our beta test team deserves particular credit Scott...

Appendix C Tutorials

We have written these tutorials to help you master the AIP4Win image-processing software program included with this book. Each tutorial walks you through activities designed to clarify and reinforce the concepts that you have learned in the book. For the best learning experience, we recommend that you first follow each tutorial exactly as we have written it. Then repeat the tutorial while experimenting and trying out new processing variations using your own CCD images. We find the best way to...

C71 Brightness Scaling

This is the most basic of image enhancement functions, and is the most frequently Astronomical Image Processing for Windows File Edt View Utilities Calibrate Measure Enhance Transform Color Multi-Image Preferences Window Help Input. Y ransfeiT Output Y Options Scalina Tyoe Input. Y ransfeiT Output Y Options Scalina Tyoe Figure C.9 Changing the value of pixels is the first and foremost technique used in astronomical image processing. Shown above, the Histogram Shaping tool modifies pixel values...

C3 Image Evaluation

In this tutorial, you will learn how to use AIP4Wirts measurement tools for evaluating image characteristics. The images for this tutorial can be found in the Image Evaluation subdirectory of the Tutorials directory on the CD-ROM. AIP4Win provides a series of tools used to examine and evaluate your images. The tools calculate image statistics, graphically display characteristics of an image, and provide a means of comparing two images. Step 1 Reading Individual Pixel Values. Let's start by...

B31 Astrometry Books and Articles

Guide to Minor Body Astrometry, Internet article at Description of how to carry out measurements and report observations of asteroids This guide is intended for those observers interested in undertaking an astrometric CCD-observing program of minor planets and or comets. Everhart, Edgar. Constructing a Measuring Engine. Sky and Telescope September 1982 279. Describes building a two-axis precision engine for measuring positions from photographs great insight into state of the art of amateur astrometry before CCDs. Konig, A. Astrometry with Astrographs. In Astronomical Techniques. Ed. W.A. Hiltner. Chicago University of Chicago Press, 1962. Quite possibly the clearest exposition of astrometry available appears in a short chapter of an impeccable source book on astronomy. March , Jordan D., II. Measuring Positions on a Photograph. Sky and Telescope July 1990 71. Instructions for doing astrometry from photographic prints includes program in line-numbered Basic for reducing x, y data using...

Advanced CCD Testing

A full set of test images for advanced CCD testing contains enough information for you to determine the conversion factor, readout noise, linearity, uniformity, and dark current as well as to check for interference and charge skimming. Advanced CCD testing is a must if you want to know for sure that your camera is delivering the high-quality images that you expect. 8.3.1 Constructing a Low-Light Level Source The purpose of the low-level light source or L3S is to provide the stable and uniform...