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Redrawing an 1888 lens

 

Dr. Hugo Schröder's concentric lens
British Patent 5,194 (1888)
US Patent 404,056 (1889)

This was the first modern photographic lens, designed in 1888. It was made possible by new optical glasses developed by Ernst Abbe and Otto Schott. This ‘aplanatic’ lens couldn't be manufactured until 1892, though, because of Schott's initial quality control problems with the exotic glass.

Meanwhile in 1889, Dr. Paul Rudolph designed an ‘anastigmatic’ lens using a combination of old glasses and new Jena glasses, but of an asymmetric form (later called the Protar), which was first to see mass production in 1890.

Some history
Ernst Abbe: Microscopy by Michael W. Davidson PhD, Laboratory Medicine, August 1, 2009
Schott's Glass by Andrea Sella, Chemistry World, April 29, 2015
The Zeiss Works and the Carl-Zeiss Stiftung in Jena by Felix Auerbach, 1904
Jena Glass and its Scientific and Industrial Applications by Dr. H. Hovestadt, 1902
The Development of the Photographic Objective by Rudolph Kingslake, 1934
Encyclopædia Britannica 1911, Vol. 21, p.509 - Photography Apparatus (Wikisource)
Dioptrique Photographique by Eric Beltrando

The original lens

A cross section of the concentric lens:

Schröder's patent doesn't describe a specific lens, but sets out design guidelines. The listed dimensions are from Eric Beltrando's recreation of the concentric lens, included among hundreds of other historical lenses at Dioptrique Photographique. Beltrando calculated some data and spot diagrams for the original lens, here. (Click on a thumbnail image to pop up a full size diagram).

A variant using modern glasses

Could this lens be replicated, say for a hypothetical project to make a simple 5x7 sheet film box camera, using currently available optical glasses?

One of the historical Jena glasses, first listed in the 1888 catalog supplement, No. 56 O.381 Dispersive Crown, is within the range of refractive index and dispersion specified in Schröder's patent. The closest modern equivalent is Schott N-KF9.

For the other glass in the new lens, several types from Schott, Ohara and others fall within the range that Schröder gave. The glass used here, N-SK16, is a bit outside that nineteenth century range of values. N-SK16 isn't a very durable glass, and so should have a hard anti-reflective coating.

My unconcentric variant with RoHS glasses, with the same 60 degree field of view:

Old and new lens formulas

Schröder's formula is more compact than mine, for the same focal length and only slightly smaller aperture, f/20. Why is this so much larger? First, because I'm a complete amateur at this. But among other things, moving the stop gives better correction but increases the diameter of the front elements.

It's still relatively small and light. People usually use f/22 or f/32 with view camera lenses, and this one doesn't need to be fast enough to show a focusing image on a ground glass. The original lens would be about 18mm (0.7 inch) in diameter for a 185mm focal length f/27 lens, and the new lens would be about 28mm (1.1 inches).

The original is completely symmetrical. My variant is symmetrical except that the stop isn't in the center. It also departs from concentricity.

Image quality

These diagrams show wavelengths from 405nm (violet) to 644nm (red).

This false-color diagram plots the total light of all colors hitting any one point. It's a purely geometric figure and doesn't show the effects of diffraction.

The on-axis geometric spot, shown above, is surrounded by a dashed circle showing the size of the Airy disk in green light at f/19 — about 0.024 mm in diameter. This is the diffraction spot that corresponds to a perfectly small geometrical spot.
(Note: This figure earlier mistakenly showed a dashed circle of 0.04mm instead of 0.024mm.)

These false-color diagrams represent off-axis geometrical image spots (neglecting diffraction) from 3.3 degrees to 30 degrees away from the center of the image. On film, spots more than about 10 degrees from the axis would begin to be a bit larger than the minimum size spot shown by the dashed outline above. Spots in the corners of the frame, 30 degrees from the axis, would be noticeably blurrier:

These charts show X and Y (tangential and sagittal) slices through each of the image spots shown above:

This "flat" diagram shows light of different wavelengths combining to make up each spot. (In this case, one dot near the center might represent many rays on top of one another.)

Resolution and Contrast (MTF):

This modulation transfer function graph shows how much contrast is preserved in the image, compared to the original being photographed, at several different finenesses of detail (here 10, 20, and 40 line pairs per millimeter at the focal plane). “0.50” means 50% contrast, etc.

Detail at 10 line pairs/mm is reproduced with a little over 80% contrast, but detail at 40 lp/mm is reproduced with only about 40% contrast. Beyond that, finer and finer detail is reproduced at lower and lower contrast, because of the effects of lens abberations and diffraction. Finally, past the diffraction limit, everything becomes a fuzzy detail-less blur.

The diffraction limit (Rayleigh limit at 9% contrast) for any f/19 lens is about 79 line pairs/mm in green light.

MTF at 10, 20 and 40 lp/mm — lens image in air, neglecting manufacturing tolerances, etc.:

MTF at the center of the image (0 degrees), about 3/4 of the way out to the corners (22 degrees), and in the corners (30 degrees). The red line approximately corresponds to the diffraction limit at 9% contrast:

Distortion is greater, at 0.33%, than in the original (which Beltrando gives as 0.08%).

Lateral color

Astigmatism

Filters

Standard filters (colored borosilicate glass) of 2.5mm or 3mm thickness, placed 1 or 2mm in front of the lens, should have no noticeable effect on image quality.

Close focusing

The lens is designed to focus at infinity. It retains good sharpness at distances down to about 1 meter, but becomes less sharp at 500mm and closer focusing distances.

 

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