The following letter is reproduced from The Luminous Landscape Discussion Forum where it was first posted. Harold Merklinger is a well regarded expert in the field of optics and author of several books on the topic. You are invited to respond to his comments there.By Harold M. Merklinger on Sunday, October 29, 2000 - 09:45 pm:
Your comparison of the Canon D-30 image quality with film is interesting, and I think perhaps not too surprising. But it does show that digital imaging is a) living up to expectations and b) will probably eventually surpass film in terms of image quality. I'd like to comment on a few specific issues.
Sharpening. I see that a few people are critical of your use of sharpening in the comparison. What they probably do not realize is that the chemical development of conventional materials involves its own sharpening. Usually called the "adjacency effect", it derives from the depletion and migration of development agents in the developer. In the absence of agitation, in highly exposed areas, the developer is depleted rapidly and hence tends to under-develop these exposed areas compared to lesser exposed areas. So far this just typifies a 'compensating' developer - leading to a lower contrast image. At the boundaries between exposed and unexposed areas, however, diffusion of the developer agent across the boundary leads to strong development of the exposed areas nearer unexposed areas, and vice versa. So, to some degree at least, sharpening just imitates what chemical development does. It is important to realize also, that the eye has its own sharpening algorithm: sometimes leading to the appearance of image characteristics that objectively do not exist. These often take the form of lines in the image that "cannot exist" under objective resolution limits.
Resolution. I generally agree that high quality photographic image is equivalent to perhaps 40 million pixels: about 5000 pixels per inch for a full-frame 35mm image, or 200 pixels per mm. This is based on consideration of resolution limited by a combination of diffraction and focus-limiting (effectively depth-of-focus). The two effects have somewhat different characteristics, however. The diffraction-limited image of an infinitesimal point of light is a softish blob. The out-of-focus image of the same small point of light is a uniformly illuminated circle or ellipse. These differences mean that an out-of-focus image of an object may still appear to have sharply defined edges, whereas a diffraction limited image of the same object will have soft edges. In the absence of focus errors, resolution is limited by diffraction: for a given diameter of lens opening, the scene being photographed is limited to a certain number of angular cells. The 40 megapixel image corresponds to diffraction limiting for about a 6 millimeter lens aperture. At larger apertures we can achieve higher resolution in a purely optical sense if the planar object is accurately imaged on a flat piece of film. But in actual pictorial picture-taking situations, depth-of-field typically limits resolution more than diffraction for apertures larger than about 6 mm. It depends upon the scene being photographed, of course. Lens flatness of field and film flatness also become significant limiters. It also turns out that this limit is nearly independent of film format. So 40 megapixels is about it for most pictorial photography.
B&W vs Colour. That 40 megapixel image is achievable with 35mm cameras with low speed black and white film like Kodak technical Pan. Colour film is only about one-third as sharp in objective testing. (See, for example John B. Williams' book "Image Clarity" or Kodak's Technical Information on Professional Products.) To the eye, the difference is not nearly so great - so important is colour to perception. So, for 35 mm images, effective pixel count is typically on the order of 4.5 megapixels (40 divided by 9) for colour images. Medium and large formats can do better, of course, approximately equalling B&W for 4 by 5 inch colour materials.
Scanning film. That 4.5 megapixel 35 mm image corresponds to only about 67 pixels per mm. The D-30 measures about 96 pixels per millimeter! Scanning a 35 mm negative at about 3200 pixels per inch is 128 pixels per mm. Looks at first glance that 3200 ppi should be adequate, but actually scanning the film image will further degrade the final image resolution. To understand this, suppose the film image consists of a single white pixel on a black background, and that we scan the image at a resolution corresponding precisely to the resolution of the film. If we happened to get the scanner's pixel grid to fall precisely in register with the film resolution grid all would be fine: the scanned image would consist of a single white pixel on a black background. In a worst-case scenario, the image and scanning grids would be offset on-half pixel in both directions: the image would consist now of 4 gray pixels - effectively half the resolution of the original image. In practice the registration is random, and the effective resolution of the scan is about 70% of the original. Scanning at twice the resolution of the image, the degradation is less: resolution is reduced by about 19%. This suggests the effective resolution of the scanned film image is about 55 pixels per millimeter: about 2.6 megapixels for the full-frame 35 mm image.
Scanning an optical image. When we scan an optical image directly - as a digital camera does - the resolution of the imaging device is the resolution, if the optical image is perfectly sharp. Of course it is not perfectly sharp - due the the diffraction and focus limits discussed earlier. The optical image will still be significantly better than the film, however. In the case at hand the 2 to 1 ratio of inherent image resolution to scanning resolution still holds, so the 19% degradation factor still applies. This suggests the effective resolution for the D-30 is about 78 pixels per millimeter. With the 15 by 23 mm sensor, the end result is effectively a 2.1 megapixel image. A significant factor, however, is that a focus-limited real image will be sharp-edged whereas the film image is limited by dye-cloud structures and such to be a more diffuse image. Using a long lens - as you did - I would expect focus-limiting to be the concern, rather than diffraction limiting. Thus I would expect the D-30 image to suffer a bit less than the above calculation implies.
End result? Pretty much a dead heat in so far as resolution is concerned.
- Harold Merklinger
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