Photographic primes

www.lens-designs.com

June 19, 2021- 243 models contributed by Bill Claff

Bill Claff has contributed 243 prime models from his website www.photonstopixels.net Amazingly, these aren’t isolated models that only exist in lens design code. Instead, Bill has correlated the disclosures in lens design patents to the lens schematics in manufacturers’ product literature. This correlation opens a wealth of possibilities, linking these design models to publicly-available data.

Japanese patent JP2014-048488 offers a good example of such correlation. Bill has shown that example 3 from this patent is an excellent match to the lens schematic shown in product literature for the Sigma 35mm F1.4 DG HSM Art lens . The figure below shows my side-by-side comparison between the Sigma product literature and my Zemax model built from the patent disclosure. Visit Bill’s page to see the two designs superimposed on one another; graphically, the match is excellent.

From left to right: photograph of the Sigma lens, Sigma's cross section of the lens, and a Zemax layout of the corresponding patent disclosure

Many other aspects of the two lenses also match well. The aspheric elements match. The “enhanced dispersion” glasses in the product literature match fairly well with the glasses with high Abbe number in the patent. The patent calls out refractive index and Abbe number, not glass types; however, these index and dispersion values match exactly to Hoya glass types. Furthermore, the elements with aspheres are of moldable glass types.

Matching lens performance was a little more difficult; vignetting is important to the lens performance but isn’t disclosed in the patent. MTF is helpful in determining the actual lens diameters. For my Zemax models of MTF, I use photopic spectral weighting and sine wave modulation; these values match the settings on the MTF stand at LensRentals.

Both Sigma and LensRentals offer MTF measurements. LensRentals is quite transparent about their MTF measurements, which seem reasonably-constructed and well-implemented. Plots of MTF vs field from both Sigma and Lens rentals are shown below, next to the same plot for the posted Zemax file JP2014-048488_Example03P. (Note that the color coding is the same in all plots) In the Zemax file, the MTF at best axial focus matches that of the MTF measured at LensRentals and separately published by Sigma. Falloff with field is significantly better in the LensRentals measurements than in the Sigma specs. The Zemax calculations fall in-between; the falloff with field is worse than the measurements at LensRentals, but better than the Sigma specs.

From left to right: Sigma MTF data, LensRentals' MTF measurements, and Zemax MTF calculations from JP2014-048488_Example03P

To achieve this good match between measurements and Zemax model, I made the fourth element the limiting aperture before the stop and the last element the limiting aperture after the stop. Neither of these apertures matched the lens diameter shown in the patent figures; this mismatch is perfectly reasonable because the patent didn’t claim anything about the apertures.

Ken Rockwell offers a thorough review of this lens from the perspective of a professional photographer. He finds the lens to be “an optically excellent lens.” This assessment agrees with the high MTF at full aperture, shown above in the lens specs, measurements, and Zemax model; but he offers more observations.

Ken notes that Bokeh “is pretty good. Backgrounds never distract.” Good bokeh is obtained from a round exit pupil with soft edges. Ken’s observation can be examined in Zemax by plotting the beam footprints on the final lens surface, giving a clue about the shape of the exit pupil. At full aperture, as shown, the beam footprints would be far from round near full field. However, away from full aperture and away from the very corner of the field, the footprints are quite round.

Footprint diagram of the last surface at full aperture.

Ken specifically looked for coma, but didn’t see any. In Zemax, the spot diagrams don’t look particularly comatic to me, either.

Ken reports that the lens “has no visible distortion at moderate focus distances around 3 to 10 feet (1 to 3 meters). It has minor barrel distortion at infinity and strong barrel distortion down at only 1 foot (30 cm).” For a distant object, this observation agrees with Zemax, which shows about -1.2% distortion at full field. For a close object, Zemax doesn’t match this observation; it shows a slightly-increased barrel distortion of -2%

Ken reports on vignetting, reporting that it’s “visible at f/1.4, and goes away at f/2 and smaller.” He does a good job quantifying this vignetting by taking photos of a uniform grey screen. Pulling these images into ImageJ, I see falloff of 55% at the corner at f/1.4. Zemax calculates a 70% falloff, somewhat worse than Ken’s observation. This difference could be caused by corrections internal to Ken’s camera or errors in my model.

Ken shows that ghost images “won't be a problem unless you go looking to cause them.” To the joy and excitement of optical engineers everywhere, Ken then goes looking to cause them, shooting “directly into the daytime sun and lightening the image by two stops to make the ghosts more visible, we can get this:”

Photo is copyright Ken Rockwell. Used with his permission.

Note the rainbow ghost image, highlighted with the red arrow.

Although Ken notes that these ghosts aren’t important for the photographer, and although he knows such things far better than I do, I still found the colored ghosts interesting, so I built a quick nonsequential Zemax file to look for them. The resultant simulation shows the bright sun in a similar part of the field as Ken’s photograph, and it shows the stray light around the sun, as well as the large, dim ghost located symmetrically about the center of the field. The ghost that most interested me, the comatic rainbow marked with a big red arrow, is also shown.

Further investigation of shows the source of this bright comatic rainbow. Light reflecting from the sensor reflects from the rear surface of the last doublet. This ray path through the lens has very little negative power, so it acts like a prim, accounting for the rainbow. This ray path also focuses the light, accounting for the brightness of the ghost. My model assumed 5% reflection on both the camera sensor and the glass surfaces; under these conditions, it calculates the irradiance on the ghost is about 10,000 lower than that of the sun.

Ken also looks for lateral color, and finds none, using his Nikon D800E camera, which corrects them automatically. Zemax calculates some lateral color; but it’s always less than half the spot radius, so it makes sense that Ken didn’t see it. None is evident in the ray fan plots below.

Ken went looking for spherochromatism, too. When looking to highlight this effect, Ken sees that “Out-of-focus highlights behind the subject can take on slight green fringes, and those in front could take on slight magenta fringes.” This effect could also be caused by some uncorrected axial color. Zemax shows no spherochromatism, but does show some uncorrected axial color - about 30um at full aperture and a distant object.

Lens Rentals offers a very different hands-on description of photography lenses. They publish “teardowns,” in which they disassemble lenses to see how they work. These teardowns are Gold for anyone wanting to learn about the engineering of photographic lenses.

The teardown for this Sigma lens shows it to be solidly made. The lens has very little plastic, and the centration seems to be achieved via hard-mounting, not adjustments. In combination with the excellent optical performance of the lens, this lack of adjustment suggests to me that the lens elements are made with unusual precision.

Lens Rental’s Roger Cicala summarizes the teardown well: “This lens is constructed very well. There isn’t the amazing heavy-duty construction of the Canon 35mm f/1.4. Instead, I’d characterize the construction of the Sigma as very efficient and carefully laid out. There’s a solid metal core with other parts all connecting directly to that core. Little touches like pegs to make sure a part is inserted in the proper rotation and shields over critical parts didn’t add much expense or weight, but show care was taken in the design. There’s nothing in this teardown that looked like a weak point.”

Be sure to check out the teardown to see the optomechanical design of this lens.

February 7, 2020 - 7 models posted from Braat and er Török's Imaging Optics

Joseph Braat was kind enough to provide not only his models, but also a detailed explanation of the models:

"Cemented doublet or multiplet lenses with extended colour correction - Examples 7.6 and 7.7

"The first example (Fig. 7.6, Imaging Optics page 434, f =100 mm, NA=0.10) has diffraction-limited performance over the wavelength range 425 < λ < 1500 nm. This wide range is partly achieved by using the Schott glass N-KZFS4 (previously KZFSN4) that shows an abnormal partial dispersion. In combination with calcium fluoride (CaF2) that has an excellent blue/UV transmission AND an abnormal partial dispersion value, apochromatic behaviour is observed with three identical axial focus positions at the wavelengths 435, 700 and 1200 nm. Note that in this doublet CaF2 plays the role of the ‘crown’ glass and N-KZFS4 that of the flint glass in a classical doublet. If the diffraction limit is respected, the field diameter is limited to 2 mm (approximately 1 deg. total field of view) because of field curvature and astigmatism.

"The second example (Fig. 7.7, Imaging Optics page 434, f =100 mm, NA=0.10, field diameter is 2 mm) is a quadruplet with FK51 the ‘crown’ glass (split over two elements), BAK2 and F2 are the ‘flint’ glasses. The best focus setting for the full wavelength range (365 to 1300 nm) corresponds to an image distance of 93.687 mm.

"Petzval and Dallmeyer portrait lens - Examples 7.19a to 7.20

"Two versions of the Petzval portrait lens are given, both using present-day glasses. Example 7.19a (Imaging Optics, page 449, f =100 mm, NA=0.14 / F#=3.6, 2x14deg) closely approximates the original Petzval lens using the glasses K5 and LF5. The Petzval lens is easily capable to resolve 20 pixels/mm at the centre of the image. At the rim of the field (25 mm off-axis) its resolution is heavily degraded by mainly field curvature (and astigmatism). Coma is hardly present due to a high degree of symmetry of the system with respect to the diaphragm. For the same reason, distortion can be maintained at a low level, typically 1% or less. The low resolution of the Petzval lens at the extreme part of the field was masked in practice by printing oval-shaped photographs instead of the current rectangular formats.

"The second version of the Petzval lens (Fig. 7.19b on the same page) is an improved design which greatly compensates for the field curvature and just suffers from astigmatism. The resolution is now comparable over the entire field. The design is called ‘strained’ as the elements show larger absolute values of the optical powers; their mutual positions and orientations are more critical as compared to the original Petzval design.

"Example 7.20 (Imaging Optics, page 450, f =100 mm, NA=0.14, 2x14deg) presents a Dallmeyer portrait lens design, with the same aperture and focal distance as the two preceding Petzval designs. The basic difference between Petzval and Dallmeyer designs is the inversion of the order of the (separated) positive and negative element in the second group of the lens system. There is no significant difference in lens performance between the two portrait lenses.

"Large-field / wide-angle photographic camera lenses and projection lenses - Examples 7.24 to 7.38

"Example 7.24 (Imaging Optics, page 458, f =50 mm, F#=4.5, 2x24deg) presents the Cooke triplet lens, composed of elements with the glasses SK16 and LF5. Colour correction is obtained by the negative LF5 central element; asymmetric monochromatic aberration and lateral colour are small as there is a high degree of symmetry with respect to the central diaphragm on the negative element. The influence of field curvature and astigmatism is reduced by the back-folding of the tangential and sagittal focal lines towards the central focus position for larger field angles. At least a thousand pixels can be well resolved over the field diagonal by this lens type.

"Example 7.28 (Imaging Optics, page 463, f =100 mm, F#=4.5, 2x32deg) is a lens system of the Double-Gauss type (US patent 1,792,917 (1927), Carl Zeiss Jena). It is a basic building block for many (more complicated) photographic and projection systems with still larger field and especially larger aperture.

"The reproduced system is capable of well-resolving 1250 pixels over the field diagonal with a relatively excellent performance towards the field rim. Thanks to the symmetrical construction with respect to the diaphragm, the distortion can be kept at a very low level (<< 1%) in such a system.

"Example 7.31 (Imaging Optics, page 468, f =60 mm, F#=3, 2x16deg) is a projection lens as they were (and are still currently) used for the display of television or computer images on a (very) large screen. The basic layout of a Double Gauss system can still be recognised in such a more elaborate projection system. The overall performance can be improved by adding extra elements, especially at the high-aperture (object) side. Note that a projection lens is commonly analysed in the high-aperture space where the modulated planar object is present, thus with the propagation direction of the light reversed. The projection lens has uniform imaging quality with a total number of 2500 well-resolved pixels on the field diagonal. From the possible aberrations distortion, astigmatism and field curvature associated with large field imaging, we just observe a residual amount of astigmatism.

"Example 7.35 (Imaging Optics, page 471, f =90 mm, F#=1.15, 2x35deg) is a projection lens for the projection of (three) cathode ray tube images (diagonal 130 mm, each with a different primary colour) onto the inner surface of a large screen that forms the panel of a closed box. The light-collecting power of the projection system has to be large, typically NA 0.40. Factors that simplify the design of the projection optics are the use of an inward-curved cathode ray tube surface, thus greatly simplifying the reduction of field curvature of the optical projection system. And, similarly, the correction of the distortion of the optical projection system by a pre-correction with opposite sign of the distortion of the cathode ray image. The total number of well-resolved pixels for each monochromatic projection lens is of the order of 2000. To obtain this high resolution at a large converging aperture, it was necessary to use aspheric surfaces with symmetry of revolution (five in total).

"Example 7.38 (Imaging Optics, page 473, f =100 mm, F#=0.75, 2x18deg) is a mirror projection system for television images that was originally developed for wide-field astronomical observation (Schmidt system). The key element is the aspheric corrector lens for the spherical aberration of the (spherical) mirror with radius R and focal distance f = R/2. The correcting (plastic) plate is positioned in the centre of curvature of the mirror, where also the physical diaphragm is inserted. This special position of the plate/diaphragm yields virtually constant correction of the spherical aberration for the (modest) field angles in this system. Of course, the system also profits from the anastigmatic imaging properties of a curved object (radius R/2) that intersects the focal point of a spherical mirror. The system allows for a very high aperture of the imaging system which is very important for astronomical observation and for the projection of TV images on distant large screens. The total number of well-resolved pixels over the field diagonal amounts to 1000."

November 28, 2017 - 47 Nikon camera lenses posted

A fun part of photography is using classic lenses. A lens may be a classic because it took iconic photographs, or because it was the first of an important class of lens , or maybe it joust had an unusually long production run and therefore found its way into many people’s hands.

Lens designers generally don’t get to use our skills in this enjoyment because lens manufacturers are generally quite coy about their lens designs. Schematics on product brochures can be misleading and the patent literature can be difficult to link to specific lens models.

For a time, Nikon seems to have revealed more than most manufactures. From 2013-2017, Nikon lens designers Haruo Sato and Kouichi Ohshita seem to have participated in a Nikon fan club, giving presentations on the history of various classic Nikon designs. Their talks seem to have been posted online for some time, in a series called “NIKKOR - The Thousand and One Nights” The series was quite charming, mentioning not only the genesis of the designs and giving sample images, but also giving a flavor of the personalities involved. Overall, it was very insightful and non-corporate; it is no longer available via www.nikon.com. [UPDATE December 25, 2020: The site seems to be available again here.]

Luckily, it’s still available via various webpage caching services, such as The Wayback Machine. To find the cached pages here, you'll need the original URL; the original postings were http://nikkor.com/story/xxxx/, where xxxxx is the note number. (For example, note 60 was at http://nikkor.com/story/0060/)

The talks included what seem to be believable links to the patent literature and believable lens schematics for unpatented designs. I was able to convert a lot of these files to Zemax models. Note that my conversion of the unpatented schematics into Zemax models is riddled with problems; I used the schematics to find the radius, thickness, and diameter of the lenses in pixels, then used real-glass optimization to find reasonable glasses, then scaled to a reasonable image size. I made no attempt to control back focal length or ensure that the glass options were contemporary to the lens designs. Still, I think the models can be instructive and useful to curious optical engineers.

November 10, 2019 - 13 models posted from the Handbook of Optics

Converting these prescriptions into models was a real chore. One of the challenges was that the prescriptions call for glass types that aren’t included in any current glass catalog, yet the text doesn’t say which catalog to use. After some searching, I found that a lot of glass types are from an obsolete Hoya catalog. The files posted are Zemax Archive files, which include this obsolete glass catalog.

Even with the proper glass catalogs, two prescriptions gave me some difficulties. The first was my transcription fault; Jakob Moskovich at Opcon Associates was kind enough to help. The second was a typographical error in the text; one surface is printed with the wrong sign; such sign errors are common in lens design prescriptions, especially in aspheres.

These difficulties provided me an opportunity to dig a little deeper into the designs. One of the designs that gave me difficulties was the 15mm f/2.8 lens (Figure 10 in the Handbook), which the authors reference to US Patent # 4,431,273-1 In the text of the chapter, the authors, who have a wealth of experience in designing lenses for fabrication, describe that they “reoptimized most of the data to arrive at ... production-ready designs,” although they give no explanation about what this modification entails. I thought that comparing the Handbook of Optics design to the patent design might be instructive.

The two lenses are very similar in form. They have the same number of surfaces and the same number of aspheres. Nominal image quality of the patent design is somewhat better, with better correction of field aberrations. Glasses are similar, too; the index, Abbe number, and partial dispersion for all glasses match nicely. Both seem appropriate for the APS-H format, with an image height of about 17mm.

The patent lens includes a plano element, which may be intended to be a filter; the Handbook doesn’t include this feature, replacing it with a powered BK7 element.

Comparing glass materials of the two designs is difficult because the Handbook design calls for an obsolete Hoya glass, including CF6. Furthermore, the patent calls out index and Abbe number, not glass type. Comparing the patent values for those in the Handbook design shows that the values differ by less than 0.02 in index and 1.2 in Abbe number.

Image quality is better on-axis for the Handbook design, but becomes worse than the Patent design over field. Lateral color isn’t very good in either design, reaching over 60um in both designs.

I didn’t compare tolerances; I think such a comparison would be unclear, considering the difference in nominal performance between the two lenses.

I found only one differences that might make the patent design less manufacturable than the Handbook lens. Its front elements are larger, especially the second element, which has an OD of 60mm, as compared to 48mm for the Handbook design. Such a tradeoff seems reasonable considering the wider field of view of the Patent design. I’m sure I must be missing something. Please write or add comments with your insight.

November 28, 2017 - 47 Nikon camera lenses posted

A fun part of photography is using classic lenses. A lens may be a classic because it took iconic photographs, or because it was the first of an important class of lens , or maybe it joust had an unusually long production run and therefore found its way into many people’s hands.

Lens designers generally don’t get to use our skills in this enjoyment because lens manufacturers are generally quite coy about their lens designs. Schematics on product brochures can be misleading and the patent literature can be difficult to link to specific lens models.

For a time, Nikon seems to have revealed more than most manufactures. From 2013-2017, Nikon lens designers Haruo Sato and Kouichi Ohshita seem to have participated in a Nikon fan club, giving presentations on the history of various classic Nikon designs. Their talks seem to have been posted online for some time, in a series called “NIKKOR - The Thousand and One Nights” The series was quite charming, mentioning not only the genesis of the designs and giving sample images, but also giving a flavor of the personalities involved. Overall, it was very insightful and non-corporate; it is no longer available via www.nikon.com. [UPDATE December 25, 2020: The site seems to be available again here.]

Luckily, it’s still available via various webpage caching services, such as The Wayback Machine. To find the cached pages here, you'll need the original URL; the original postings were http://nikkor.com/story/xxxx/, where xxxxx is the note number. (For example, note 60 was at http://nikkor.com/story/0060/)

The talks included what seem to be believable links to the patent literature and believable lens schematics for unpatented designs. I was able to convert a lot of these files to Zemax models. Note that my conversion of the unpatented schematics into Zemax models is riddled with problems; I used the schematics to find the radius, thickness, and diameter of the lenses in pixels, then used real-glass optimization to find reasonable glasses, then scaled to a reasonable image size. I made no attempt to control back focal length or ensure that the glass options were contemporary to the lens designs. Still, I think the models can be instructive and useful to curious optical engineers.

March 8, 2017 - 38 new lens models posted

This posting includes fisheye, wide-angle, and macro lenses. Despite the large number of samples and wide time range, there is relatively little overlap in the apparent application space.

The most-similar designs seem to be U.S. Pat. 9,182,570 & U.S. Pat. 4,647,161. Both are f/3.7. Both have a similar ratio of image height to focal length. The newer lens has more elements and has about 1/2 the spot size, measured as the ratio of RMS spot size to image height. The older lens is well-corrected for f-theta dsitrotion; the newer lens obtains a wider field of view by allowing 2% f-theta distortion.

The older patent is filed pro se, meaning that it isn't assigned to a company. The inventor, Rolf Muller is a German engineer who had one other lens design patent, also as a pro se inventor. I found no evidence of him marketing his lenses. I wonder what his story is.

January 26, 2017 - 40 models for smartphone lenses posted

I can never decide if I should follow these patents or not. Sometimes I think I should follow them because the lenses are ubiquitous, becuase they take so many of the pictures we care about, because they’re unlike any other class of lens, and because there isn’t too much written about them outside the patent literature. Usually, though, I think I should ignore the patents in this field. There’s way too many patents to follow; Largan alone has over 300 patents in the field. The designs don’t seem very instructive for other optical designs; most designs of this category have gross aspheres, including lenses with sombrero-shaped surfaces. The product lifetimes are quite short. Also, I have a feeling that the properties that make one of these designs better than others aren’t readily captured in simple models; alignment sensitivity and stray light can be particularly problemmatic for these systems.

The only good overview papers I’ve seen on the topic are Peter Clark’s papers from IODC 2014 and IODC 2006. He does a good job of demonstrating the amazing small size of these lenses, as well as the difficulties in manufacturing and testing them.

I see a two trends in the designs. First, I see a progression from three-element designs to five element designs; six element designs are common in more-recent patents. Next, I see that earlier patents used glass and a mixture of lower-technology plastics like styrene and polycarbonate, while newer patents use all-plastics, with higher-tech plastics such as COC.

To get an idea of the image quality for these lenses, I wanted to build a model for the lens that’s in a widely-available, high-quality handset. Such information isn’t available from reviews or from manufacturers. However, reviews and manufacturers readily publish information such as sensor size, f/#, effective focal length, and number of lens elements. For example, a little googling will show that the iPhone 5 has the following specs: f/2.2, efl=4.1mm, image height of 2.7mm, 5-element lens. U.S. Pat. #8,934,179, example 4 has specs that match these pretty well, and is assigned to Kantatsu; Kantatsu supplies a lot of lenses to Apple. This nice matching certainly doesn’t mean that the lens file US08934179-4.zmx matches the lens used in the iPhone 5. I suppose that several different lenses were used in the iPhone 5, and none of them match this design. However, I have a feeling that the Kantatsu engineers had the Apple specs in mind when they developed the designs in this patent.

For an example of the excellent performance of these lenses, look at US08934179-4.zmx. RMS spot size is near the diffraction limit across the entire field, and lateral color is well under the diffraction limit across the entire field. This performance is broadly consistent with the amazing sharpness and color of my iPhone 6. I hope to present some of these measurements at IODC 2017.

What do you see in the designs? Do you have insight into the differences between the designs or how the designs evolved? Please participate in the Comments section.

October 12, 2016 - 40 models for telephoto lenses posted

Today I posted 46 lens files for telephoto lenses. The patents are by the usual cast of Japanese photographic suppliers. Although the files include disclosures from recent patents, very few aspheres are used.

The posting includes both catadiopric designs and all-refractive designs. The catadioptric designs have a reputation for poor image quality, but comparing two contemporatneous designs of similar focal length (US04951078-1 and US05323270-5) shows that both designs have similar RMS spot sizes.) Other considerations, especially f/# and bokeh, are likely to enable better photographs with the all-refractive design.

I did a little analysis of the glass types used in the disclosures. After removing double-counting from the catadioptric lenses, the models have 453 glass surfaces. The table below shows the most-commonly-used glass types. Unlike other lens sets I've posted, these lenses use a lot of BK7, mostly in the catadioprtric designs.

Example nd Vd # of occurences

N-BK7 1.52 64 49

SFL6 1.80 25 33

S-FPL51 1.50 82 32

J-FKH1 1.50 83 31

N-FK5 1.48. 70 20

SF57 1.84 24 19

LASFN7 1.78 50 16

TAFD5F 1.84 43 13

September 14, 2016 - 19 fisheye lenses posted

Today I posted 19 lens files for fisheye lenses. Modeling these lenses presents special challenges; in Zemax, be sure to use robust ray aiming with real rays. One special file is US03737214-1, which looks like the schematics for the Nikkor 6mm f/2.8 Fisheye, which has a 220 deg field of view. Several awestruck reviews are available online, like this, this, and this.

An excellent paper on fisheye lenses, “Design issues of a hyper-field fisheye lens,” by Chadwick Martin, gives a convincing rationale for using a front element with a high Abbe number; but some of the disclosed designs, such as #8,456,765, don’t follow this advice.

October 30, 2015 - 95 full-frame photographic objectives posted

These patents are assigned to 11 different companies, all name-brand photography companies. The Abbe diagram below shows the distribution of glasses used in the disclosures, and the table below lists the most-common glass types. Heavy use of both high index and low-index glass is evident. Comparing this glass list to the most-common glasses disclosed in folded zoom lenses shows some overlap at the index extremes, but comparatively little use of moldable materials.


nd Vd usage example

1.855 24 7% N-SF57

1.505 83 5% E-FKH1

1.775 50 5% LASFN7

1.795 47 4% LAFN21

1.835 43 4% TAFD5F

1.815 25 4% SFLD6

1.505 82 3% PFK80,

1.885 41 3% TAFD30

I also find it instructive to look at the distribution of paraxial properties of the lenses. The 2-dimensional histogram below shows the frequency of various focal lengths and f/#. By far the most-common combination is f=50mm, f/1.4. This result makes sense because this combination is one of the most common (and most useful) lenses for most photographers, with a crop factor = 1.

Taking a closer look at these typical f=~50mm, f/~1.4 lenses shows that they typically have 7 or 8 elements, typically with no aspheres. This typical lens is double-gauss, too. One exception in this range is #8,964,096, from Sony, which is still quite similar to a double Gauss. Its closest match, #7,706,087, from Nikon, has the same number of elements, but one less asphere; it's also a much more typical double-gauss construction.

February 28, 2015 - 18 new photo primes submitted by Steve Eckhardt

The new models include designs based on the double gauss and modified triplets. These submissions are based mostly on older designs, before 1960 or so. Many designers prefer to use these older designs as starting points.

The new models also include more modern designs, mostly wide-angle lenses. These submissions are from newer patents, mostly from the 1990s. I prefer this era for starting points because the glasses were relatively modern, yet aspheres weren’t as common as they are today.

November 19, 2014 - More than 400 files posted, based on Cox

More than 400 new files were uploaded today, in Zemax and Oslo formats. The files are based on Cox’s “A system of optical design.” In his classic text from 1964, Cox spends about 500 pages describing his method of optical design, then provides about 300 example designs, mostly from the patent literature. Cox’s system separates lens designs into twelve types, and he includes examples of 9 types

  • 1 - telescope objectives

  • 2 - telescope eyepieces

  • 3 - nearly symmetrical and derived types

  • 4- triplets and derived types

  • 5 - Petzval lenses

  • 6 - Telephoto lenses

  • 7 - inverted telephoto lenses

  • 9 - wide angle lenses

  • 12 - special systems and aspheres

The uploaded files update Cox’s tabulated designs in several ways: sign errors are corrected, misplaced stops are often corrected, real glasses are generally used, and apertures are defined. Even with these updates, most of the models are will probably need reoptimization before they’re very useful. Nevertheless, this large set of designs has long been an important part of experienced designers’ toolbox.

Cox’s designs are obviously dated; the newest one is from 1961. Today we obviously have much better design tools, but we also have a much wider selection of glasses. To compare the glass usage then and now, I compared the glasses used in Cox’s designs to glasses used in folded zoom lenses, as presented in a paper I gave at IODC 2014. Both sample sets included about 1100 materials. This table shows the most-commonly used glasses in Cox:

nd Vd usage example

1.625 60 11% SK15

1.655 34 7% SF12

1.695 55 6% LAK9

1.725 48 4% LAF3

1.725 29 3% SF18

1.695 31 2% N-SF15

This table shows the most-commonly used glasses in folded zoom lenses:

nd Vd usage example

1.855 24 13% N-SF57

1.505 82 5% MC-FCD1-M20

1.535 56 5% E48R

1.885 41 5% N-LASF31A

1.925 21 5% M-FDS1

1.495 70 4% FK5

There is no overlap between these materials at all. This difference makes sense because the zoom lenses are high-volume lenses that should make the most use of modern, moldable materials. However, notice that there is also very little similarity in the index and Abbe number, indicating the huge advantage presented by modern materials. Notice that the modern sample has 4X greater range in index and 2X greater range in abbe number.

What do you notice in these classic designs? How have you used Cox’s examples? Please participate by sharing what you’ve learned.

September 5, 2014 - 25 Double Gauss files posted

The double gauss is one of the most widely-studied design forms, and has found uses well beyond its initial photographic application. Good summaries of the commercial aspects of the design can be found on Wikipedia, or LensRentals.com

For historical reasons, I included a model of the original patent, 583,336. The patent is the basis for many commercially-successful designs, but Wikipedia claims that its original product, the Zeiss Planar, had limited commercial success for many years. AR coatings hadn’t been developed, so the lenses suffered from excess flare.

Here are some fun and/or instructive things to do with these files:

- Look up the original patent: Notice that the glass definitions don’t use Abbe number. Notice that the glasses available at the time had quite low index (n<1.6) Also notice that the lens prescription doesn’t really follow the way we describe designs now.

- Download the file built from the original patent. I used modern glasses with the same index and dispersion as the patent disclosure. I thought it was fun to see how much better the image quality could get, just using the default merit function from Zemax, even maintaining the symmetry and glass choices in the patent.

- Compare the original patent to a more modern one of similar design. For example, patent #6,366,412, from 2000, has the same number of elements, no aspheres, and reasonable glasses. Its image quality is about twice as good as the original. (Don’t forget to scale for focal length.)

- Compare the original patent to the most-modern design. Patent 8,427,765 has about half the f/# as the original patent, and one less element; but it uses high index glasses and an asphere to obtain much better image quality (although the field of view is smaller.)

What do you see in these files? Share your insight in the Comments section. Do you have lens design files you’d like to share? Please participate in building the site.

Summary of designs

Summary - primes



Design files