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 telescope in a regular grid, with each element in the grid represented by a single numerical value.

The number of photons captured by a photosite is proportional to the flux of photons times the collecting area of the photosite, and the number of electrons generated is the product of the quantum efficiency and the number of photons. Given that n is the average number of electrons generated, because the photons arrive at random, the number of electrons generated by a photosite during any particular integration is n±Jn, and the signal-to-noise ratio is Jn .

The ability of CCDs to store charge during an exposure ranges from 30,000 to 500,000 electrons in the charge well; so the expected random variations are 173 and 707 electrons, respectively. In addition, reading the charge from the CCD

Image at f!24 Image at f!48

Image at f!72

Image at f!24 Image at f!48

Image at f!72

9,u Pixels (Critical) 9/x Pixels (Oversampled) 9ß Pixels (Oversampled)
18|U Pixels (Undersampled) 18/u Pixels (Critical) 18,u Pixels (Oversampled)

27ß Pixels (Undersampled) 27/j. Pixels (Undersampled) 27n Pixels (Critical)

Figure 1.18 Matching pixel size and telescope focal ratio is essential for high-resolution imaging. The top row shows highly enlarged images at the focal plane of telescopes used at f!2A, f/48, and HI2, with an effective wavelength of 730 nm. The succeeding rows show the same images as captured by detectors with 9-, 18-, and 27-micron pixels. At a focal ratio of f/24, 9-micron pixels satisfy the Nyquist sampling criterion, with two pixels across the Airy disk. With 18-micron pixels, the image is critically sampled at fl48, and with 27-micron pixels, critical sampling occurs at f/72. Images with finer sampling are called oversampled; those with coarser sampling are called undersampled.

27ß Pixels (Undersampled) 27/j. Pixels (Undersampled) 27n Pixels (Critical)

Figure 1.18 Matching pixel size and telescope focal ratio is essential for high-resolution imaging. The top row shows highly enlarged images at the focal plane of telescopes used at f!2A, f/48, and HI2, with an effective wavelength of 730 nm. The succeeding rows show the same images as captured by detectors with 9-, 18-, and 27-micron pixels. At a focal ratio of f/24, 9-micron pixels satisfy the Nyquist sampling criterion, with two pixels across the Airy disk. With 18-micron pixels, the image is critically sampled at fl48, and with 27-micron pixels, critical sampling occurs at f/72. Images with finer sampling are called oversampled; those with coarser sampling are called undersampled.

adds 6 to 50 electrons of random noise. When we apply the photometric bit-depth equation, we find that a normally exposed CCD image contains from 7 to 8 bits of useful information. However, to distinguish n gray levels containing that useful information requires a 12-bit to 16-bit analog-to-digital converter.

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