Photography: Appreciation through Understanding

Pixel size, F-stop, and resolution

Comments[7] 02:20PM Feb 15, 2007 by Charles in General

        There has been a good bit of discussion about the practical value of pixels on a sensor that are smaller than the size of a diffraction spot.  It turns out that the size (diameter) of a diffraction spot measured in microns, e.g. the size of the image of a star taken with a diffraction limited lens, is about 35% larger than the numerical value of the F-stop used.  One view is that the best resolution is obtained when the diffraction spot diameter is about equal to the pixel diagonal (1.414 x pitch) or the F-stop is about equal to pixel width (pitch), and that the pixels are wasted when larger F-stops (smaller apertures) are used.  Another view, is that, in the presence of diffraction broadening, pixels smaller than the F-stop by a factor of two or three give an advantage in resolution over pixels that match the F-stop.  When the F-stop is larger than the pixel size by factors of five or more, I think everyone agrees that pixel size has essentially no effect on resolution.

        Do these considerations have any practical consequences for photographers?  In fact they do in situations where lenses are stopped down to increase the depth-of-field (DoF).  To be precise, a circle of confusion (CoC) must be selected in order to compute the DoF.  The traditional method has been to select a CoC based on the acuity of the human eye and the size of the final print.  For example, a typical choice is use a CoC that is equal to the diagonal divided by 1500.  Another choice, that has some merit in digital photography, is to set the CoC equal to the pixel size and to demand maximum resolution at the expense of DoF.

     But suppose that the photographer compromises on resolution in favor of DoF and uses an F-stop that is perhaps 3 times the pixel size.  What would be the effect on resolution if his pixels were larger so that the F-stop was only twice the pixel size?  I have tried to answer this question with some simple experiments.  I used both a Canon 10D (pixel width = 7.38 microns) and a Canon Rebel XTi (pixel width = 5.74 microns) to photograph a portion of a standard resolution test chart containing vertical lines with gradually decreasing spacings.  In the image on the sensor, the lines at the right end had spacings of about 13.9 microns.  A Sigma 105mm macro lens was used and the F-stops ranged from 4 to 32.  Also, the cameras were mounted on a steady tripod, mirror lockup was selected, and RAW images were acquired.  In the Adobe Camera RAW conversion the default sharpness and the color noise reduction were both set at 25

     The cropped results are shown in Figure 1 (10D) and Figure 2 (XTi).   I conclude that the XTi provides more resolution from f/4 to f/22, but at f/32 the pixel size makes no contribution to resolution.  Even at F/22 the XTi yields better resolution than the 10D, or pixels four times smaller than the F-stop are better than pixels three times smaller.  I think that this is an example of the advantages of over sampling that has been discussed by Wallis.  Unfortunately, the properties of the anti-aliasing filters used in the cameras is not known.

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