The Current State of Affairs

One of the most difficult tasks facing the photographer about to buy his or her first digital camera is the issue of image quality or IQ as I call it. No other hi-tech field has done as poorly in defining the basic qualities of the products they sell as the electronic camera industry. The hi-fi stereo industry has a bevy of meaningful the prospective buyer ccan use to judge the relative merits of an amplifier or set of speakers that are candidates for purchase. While not perfect, these numbers give one a place to start. The prospective buyer of a serious pro lens can look at MTF {modulation transfer function} charts made available by many makers to look at. For the initiated, these provide meaningful information about lens contrast and sharpness under varying conditions. The digital camera industry normally issues one statistic, the number of megapixels the sensor captures-- about as meaningful as the maximum possible speed indicated on your cars speedometer. But we may now have a better way to describe image quality.

Korens Hypothesis

At the roots of the electronic comunnications industry is Claude Shannon's ideas on information theory. His classic equation defining the transmission capacity C of a data channel is,

C = W log2(SNR+1)

C the data capacity is usually measured in bits per second. The photographic equivalent is image detail. This includes both the actual numbers of pixels you see in an image and their quality or tonality. A color image has more information than a B&W image and as such requires more capacity to capture and display.

W is the bandwidth of the channel in hertz. This corresponds closely to the optical 50% MTF frequency f50. The higher the MTF 50, the higher the perceived image sharpness. Lenses, electronic image sensors, film and even printers have their own MTF characteristics.

SNR is the signal-to-noise ratio . Film grain is the film equivalent of electronic noise. SNR is difficult to measure in the world of film photography. Kodak uses a system it calls print grain index to measure grain. The SNR of a photo depends on the overall range of luminosity in an area of the photo and the size and luminosity range of the grain in that area. SNR is highest, in contrasty detailed areas, like those seen in the B&W MTF currve you see on the left. It is lowest, and hence noise/grain is most visible, in smooth areas like the cloudless blue skies of a desert landscape image.

A study of scanned images by R.N.Clarke has shown that if MTF was the only factor effecting image quality it would take about 12 megapixels for a digital camera to equal 35mm photos shot with a fine grain modern film. However noise/grain effects the overall quality and plays an important role. These relationships led my friend Norman Koren to make the following conjecture which I call Koren's hypothesis.

IQ = W log2(SNR+1)

Perceived image quality, IQ is proportional to total information capacity, which is a function of both W, which is the image visual capacity in one dimension (sharpness) and noise (grain).

W = MTF 50 * sensor size

W is the product of MTF 50 and image sensor size. MTF 50 is measured in line pairs/mm and the sensor or film size is measured in mm. If the image is recorded on film, the film size replaces the size of the sensor. MTF 50 can be calculated for the camera system by using a combination of lens data, sensor or film data, and a computer based mathematical model. SNR depends on the luminosity range of the pixels in the image,usually 256:1 for 8 bits per color RGB pixels and the noise/grain as measured in the image.

The image quality of digital cameras will equal 35mm with fewer pixels than predicted by MTF alone because digital cameras with large sensors--all the pro-level SLR's-- have much less noise.
Skies in digital camera images are virtually grainless. That makes a big difference in perceived quality. Many photographers will perceive images from the current generation of high-end 6 megapixel cameras-- the Canon EOS D60 and the Nikon D100-- to be equal to 35mm. We are there now! On the other hand digital cameras with very small sensors --the point and shoot variety-- have significant noise, even if they have the same number of pixels.

About The Calculations

The MTF 50 image sharpness calculations for the camera systems were performed by Norman Koren. Norman used manufacturers lens and film MTF data and established models for CCD and CMOS sensors to perform his calculations. The data was fed into his Mathworks based camera system model on his home PC. The model depends on both the film or sensor type and the height of the film or sensor exposed to create the image. The computer model calculates the image sharpness MTF 50 number in line pairs per millimeter. W the overall image optical bandwidth can then be calculated by multiplying the MTF 50 number by the sensor height in mm. Sensor or film height data was as specified by the manufacturer and not actually measured.

The SNR was calculated by me from actual digital images loaded into Adobe photoshop. I used film images shot by myself and scanned on a NIkon LS8000 scanner at 4000 DPI for the Provia 100F and Velvia SNR numbers. Digital images from the Digital Photography Review tests of the Nikon D100, Canon D30 and D60 were used for noise measurements of those cameras. The noise measurements for the Sony F707 were taken from pictures I've shot with an actual camera I have.

I selected and cropped out a 50x50 pixel test patch of clear uniform blue sky with the Photoshop crop tool. The Image|Histogram tool was then used to create a Histogram of the test patch. I tried to select an area that is roughly of zone 6 luminosity (light grey if you're unfamiliar with the zone system). The standard deviation of the luminosity channel is the noise RMS value. An ideal test section of uniform color should have a deviation of zero. The same section sampled by an analog/digital converter should have a standard deviation of 0.5. The A/D converters used will always have rounding or quantatization error of + or - 1/2 the least significant bit. The maximum value the signal can have for an 8 bit per color image is 255. The range of signal spans 256 values from 0 to 255.

Based on these factors, that maximum SNR vlaue possible for a standard 24 bit digital image is 256/0.5 or 512. Some digital cameras came very close to this number. The Canon D60 was best with a SNR of 345.The Nikon D100 followed very closely with a SNR of 308. I used patches of blue for two reasons. One, I am a landscape photographer and the quality of blue skies is very important to me. The second is most image sensors tend to have more noise in the blue channel.