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How many pixels does a film frame contain?
Is film photography coming to an end?
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"The report of my death was an exaggeration."
Mark Twain

First serious expectations of an end to film photography were aroused, when 6 Mpix image sensors appeared on the market. Optimists said such a huge number of picture elements are quite enough. "Yes, that is right!", — marketing experts started forming public opinion.

Another severe blow to chemical methods of producing images was delivered on February 11, 2002. On that day, the world was told about Foveon X3, an image sensor of a new type. Before that, all image sensors were mosaic-based (see the picture). Each pixel could capture only one color. The missing information about colors was reconstructed with the help of interpolation algorithms. Foveon X3 was claimed to gather information about three basic colors in every picture element.

Commenting this promising technology, Carver Mead, Foveon's founder, said in the interview to New York Times (February 11, 2002):

Foveon's web-site contains more cautious words. Their FAQ informs us that

Now the activities related to Foveon X3 are not that noisy. Still, many people in the world of photography continue to discuss digital technologies. And new forecasts about the date when the film photography will die are constantly appearing.

We are not going to predict events in this article. Let us get down to more prosaic things, and answer the question: how many pixels are there in a frame of a 35 mm film? Do not be afraid! We are not going to be very theoretical. Using our common sense, we will derive the results from the well-known facts. The answer will be received by two different approaches.

1. The most simple and obvious approach

According to experts (oh, yes, this phrase is always used to avoid boring explanations and to make one's words more significant :-) ), there is no need to scan film with a better resolution than 4000 dpi. A lot of professional film scanners operate at this resolution. Of course, there are more precise devices on the market. But many people say 4000 dpi is enough for many purposes.

This resolution is equivalent to approximately 150 pixels per mm. The 24 x 36 mm frame will contain approximately 20 million such pixels. Now we have the answer.

2. A more accurate approach

Let us derive the answer from the information about the real resolving power of a combination of a good lens with a good film. Such an approach does not pay a lot of attention to the causes, such as the Nyquist theorem, aliasing, film grain, optics and so on. It concentrates on the final cumulative result.

In this article we will use the data from Norman Koren's web-site, a good source of information on the resolution issues. At the end of "Understanding Image Sharpness / Part 1" he obtained the combined response for the Velvia film and the Canon 28-70mm f/2.8L lens. The 50% and 10% points for MTF appeared to be correspondingly 36.8 and 68.6 line pairs per mm. (If you are not familiar with MTF, please read my Introduction to the Art of Understanding MTF or Mr. Koren's entire article.)

Only pessimists would determine resolving power at a level where MTF is 50%, while the 10% level looks excessively optimistic. The truth is somewhere in between. It is reasonable to suppose that the "film plus lens" system has a resolution of approximately 50 line pairs per mm. Please note that this is not the extreme value, but quite a realistic estimation.

Now let us answer another question: how many pixels does it take to represent a line pair. Mr. Koren discusses this question at the very beginning of Part 2. Two pixels are not enough, while the number four seems somewhat pessimistic. Mr. Koren prefers three pixels to resolve a line pair. So does the Sony Company. Quite a long lime ago, they suggested that 3 pixels per line pair be used to estimate the resolving power of video images ensors.

Let us share the opinion of both Mr. Koren and Sony. If we multiply 50 line pairs per mm by 3, we will get the same 150 pixels per mm. Again, each film frame contains 20 million pixels.

Conclusions

When we have a 24 x 36 mm imaging sensor containing at least 20 million pixels, we will say that the end of film technologies is not far off.

Sometimes people say that such a high resolution of film is not needed in many cases. That is true. But "in many cases" does not mean "always".

Brief comments on film scanners with 2700 dpi

Such devices are widespread. They cannot derive the entire information from film, still they are very useful.
Since the 300 dpi resolution is required for printing, such scanners can be used to magnify film frames by
9 times. As a result we can get pictures as large as 20 x 30 cm (8" x 12").

There is another useful fact to remember: the circle of confusion in film photography typically equals 0.03 mm. It shows how large an image dot can be to be considered as an elementary point. When a picture is scanned at 2700 dpi, the pixel size is one third of the diameter of the circle of confusion. Thus, 2700 dpi is quite suitable for many purposes.

The resolution of 4000 dpi is needed when we deal with great enlargements or some special quality requirements. In all such cases, photographs should be taken based on a smaller circle of confusion.
A film frame that is scanned at 2700 dpi contains 9.7 million pixels. This is the absolute minimum for the estimation of how many pixels there are in a 35 mm photo image.

September 23, 2002

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In Part 2 you can read FAQ related to this article.

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Links

1. If you are looking for a mathematically rigorous deduction and more details, please read "Understanding Image Sharpness" by Norman Koren.

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