Modulation Transfer Function (MTF) and Subjective Quality Factor (SQF)

Part 5: SQF and Popular Photography

While we can state SQF to any degree of precision (e.g. 95, 95.1, 95.123 etc.), Grainger found that it really takes about 5 points difference before most viewers notice a difference in image quality. So while most viewers would not notice a difference between images with SQFs of, say, 88 and 90, most would notice a difference between, say, 88 and 93. This is indicated in the Popular Photography lens tests by the different color shading of the SQF values and the A+, A, B+, B etc. ratings which are spaced by 5 SQF units, as shown in the example below.

Since SQF is derived from MTF and as we saw earlier every point in an image has its own MTF characteristic, so every point in an image has its own SQF properties. In order for SQF to be useful it needs to address the whole image. To do this, the Popular Photography test splits the image into three regions. The center of the image accounts for 50% of the final SQF. 30% of the final SQF is determined by the SQF at a point 50% way between the center and the corner and 20% of the final SQF is determined by a region 80% of the way to the corner. At each point radial and tangential measurements are averaged.

For example suppose we calculate an SQF of 90 in the center, 81 50% of the way to the corner and 60 80% of the way to the corner. The combined SQF would be (90 x 0.5) + (80 x 0.3) + (60 x 0.2) = 81, and that's the number you'd see in the lens test - 81

Of course you'd also get an SQF score of 81 if the SQF were 81 at all points in the image (81 x 0.5) + (81 x 0.3) + (81 x 0.2) = 81. You still get an 81 with an SQF of 100 at the center, 90 at 50% of the way to the corner and only 15 at 80% of the way to the corner (100 x 0.5) + (90 x 0.3) + (15 x 0.2) = 81. This again shows up the problems of a one number measurement. It doesn't tell you how the image quality is distibuted across the frame.

Whether MTF of SQF is a more useful measure of lens quality depends on who is reading the results. MTF curves are more complex and more difficult to interpret, but they contain more information. The problem is that if you don't understand them, either they are meaningless to you or may even mislead you if you don't know that you don't understand them! SQF on the other hand was designed to be a simple system which anyone can understand. It reduces image quality to a single number again, so it's not (nor is it intended to be) a technical measure of optical quality. It's a number which a typical consumer can use to get some idea of the relative overall quality of images shot with different lenses at different apertures and printed at different sizes. Though it's an objective measurement, it's based on human visual response as well as the intrinic quality of the image formed by the lens, and so may preduct a subjective response to image quality.

As single number SQF value is probably more useful than a single number MTF value because it at least factors on the characteristics of human vision, though a detailed MTF plot contains much more information which will enable a skillful and educated reader to better evaluate a lens. However, for the non-technical reader, a comparison of SQF values may be more useful than plots which they don't really understand, and SQF certainly provides an easier, if less detailed, metric for comparing lenses.

References

[1]"An optical merit function (SQF) which correlates with subjective image judgments", E.M.Grainger and K.N.Cupery, Photographic Science and Engineering, Vol 16, #3, pp221-230 (1972)

[2] "Lens performance assessment by image quality criteria", K. Biedermann and Y. Feng, Image Quality: An Overview, Proc. SPIE Vol. 549, pp36-43 (1 985)

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