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Applying an Abbe Criterion to Photomacrography
by  Ted Clarke, Scientific Photographer and Instrument Maker

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Microscopists are generally familiar with Abbe’s criterion for useful magnification being between 500 and 1000 times the numerical aperture. This subject and its relation to digital imaging are covered in my previous Modern Microscopy article “Pixel Array Size Requirement to Replace Photomicrographs on Film”.  Since the readers of this article are most likely to be microscopists, the intent of this article is to show how the Abbe criterion can be applied to photomacrography over a magnification range between 1X and 50X. The macro lenses used for photomacrography have iris diaphragms calibrated in f/numbers or exposure factors (in the case of Zeiss Luminar lenses) and the problem for the scientific photographer is what aperture setting to use when the subject is three dimensional and the usual goal is to have the entire depth of field in focus, which is more difficult as the magnification increases. These macro lenses can be used over ranges of image magnification for which they are aberration corrected, making their numerical aperture a function of both the diaphragm setting and the camera magnification. The term numerical aperture, N.A., is not common in the literature on photomacrography. The purpose of this article is to show by example that an Abbe criterion chosen within a three f/stop range provides a good balance between image resolution and depth of field. The examples cover a magnification range of 1X through 50X, including contact printing of 1X negatives through 50X digital images. The three f/stop range corresponds to an Abbe criterion of final magnification between 320 and 660 times the N.A. The equations for calculating the f/stop values are given in Table 1. The mathematical basis for Table 1 is given in Appendix I: Resolution Considerations for Photomacrography, a shortened version of my article on the subject in Microscopy Today 1.

 

TABLE 1
Max Resolution of Final Image
Abbe
Criterion
f/number
Depth of Field
mm for
8 lines/mm
Depth of Field
mm for
6 lines/mm
Depth of Field
mm for
3 lines/mm

9 lines/mm
0.11 mm
(0.22 mm Airy Disk)

320 N.A.
160/(MTot+Menl)
38/MTot2
85/MTot2
200/MTot2
7 lines/mm
0.15 mm
(0.29 mm Airy Disk)
440 N.A
220/(MTot+Menl)
--
70/MTot2
260/MTot2
4.5 lines/mm
(0.44 mm Airy Disk)
660 N.A
330/(MTot+Menl)
--
--
330/MTot2

 

The first experiments were with a finely detailed graphic arts pattern mounted on a 45 degree incline shown in Figure 1. The pattern was photographed with a 35mm camera at magnifications of 1/8X, 1/4X, 1/2X, and 1X. An Olympus 50mm focal length macro lens was used for apertures between f/8 and f/22. A 50 mm focal length enlarging lens modified to use inserted Waterford stops in place of the iris diaphragm, shown in Figure 2, was used for apertures between f/25 and f/100.

 

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Figure 1
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Figure 2

 

The half of the field below the focal plane of the camera lens was recorded at 1X using two exposures to cover the field width, followed by contact printing and splicing the two images together to make the montage shown in Figure 3. Figures 4-6 show the other montages for the patterns recorded at lower magnification and subsequently enlarged to 1X during printing of the negatives.  These montage images are from scanned slides taken of the original montages published in my 1984 article in The Microscope 2.

 

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Figure 3
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Figure 4
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Figure 5
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Figure 6

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