March 26, 2023 - Five models , from a new contributor

John Hygelund shared five mobile imaging models, based a paper by Steinich, transcribed as part of an assigment at the University of Arizona. The designs represent a curation of cellphone lens patents as they've progressed from 2003-2021. John notes that, "Design use index and Abbe numbers are generally consistent with plastic optical materials. The surfaces are highly aspheric with generally with terms 8th to 14th order. The track length is also generally less than 6mm. All design have f/# of ~2.8. As with many patents, the given prescription is not necessarily optimized. "

July 1, 2022 - *more* models contributed by Bill Claff

Today I posted more models from the prolific Bill Claff, from www.photonstophotos.net    These models have a heavy emphasis on older products, many of them now treasured classics.

Photographers’ reactions to older lenses like these often seems contrary to lens designers’ experience.  Lens designers’ goals of higher MTF, lower distortion, less stray light, more uniform illumination and less chromatic aberration are  not necessarily appreciated by professional photographers.  These photographers like to use lenses to create art, which often creates beauty from imperfections.  Sometimes this artistic creation is aided by the physical feel of the lens, which an engineer might quantify as mass and torque.  Sometimes it’s aided by the desired bokeh, the character of the out-of-focus spots; an engineer might try to quantify such character might by the shape and distribution of these out-of-focus spots.  Sometimes the photographers appreciate the effects of the poor coatings in older camera lenses, which cause flare and color effects that an artist can use to make a plain photograph much more beautiful.

Unfortunately for an optical engineer, the language used for these artistic qualities is often poorly linked to typical measures of optical engineering.  For example, B&H describes that vintage lenses “render subjects like portraits and landscapes in a distinctive and appealing way that can’t quite be conveyed in words.”  PreiumBeat describes that “You can expect to see vignetting with most older lenses. While some would argue that vignetting is a bad thing, it can sometimes create an interesting effect...The distortions created by shooting on vintage glass can be incredibly stylish and unique.“  On MyClick, Krista Roth  has some excellent images showing the beautiful effects that artists can get from lens flare.  She also explains “Vintage lenses are known for capturing amazing sunflare, haze, and magical light. Since vintage lenses don’t have the protective glass covering that new, modern glass has, they filter light differently. They let in more light, and light anomalies are allowed into the lens which can produce large colorful sunflares, unique haze, and interesting bokeh.”  Her language is beautiful, and so are her photographs.  I wondered if I could make some correlation between such language and precise calculation in lens design code.

To investigate this correlation, I thought it might be instructive to compare the engineering aspects of some vintage lenes to some modern lenes with similar properties.

For a baseline vintage lens, I chose the Olympus Zuiko Auto-T 100mm F2, which was introduced in 1980. (US004435049-Example05P )  This vintage lens seems to be in high demand these days, commanding prices of up to $1800 on eBay. Online reviewers rave about it, often in terms that are poetic and difficult to quantify.  For example, Lightstalking says it has “amazing sharpness even wide open, color is vivid and accurate and bokeh is creamy and smooth. This superb lens even has a floating rear element to suppress distortion.”  Phillip Reeve shows some beautiful images he’s taken with it.  He also notes that “Bokeh is one of the biggest strengths of this lens, it is just always super smooth.”  and that “There is a moderate amount of lateral CA.”  He finds sharpness a particular strong point.   He doesn’t like flare, though, describing flare “not the best performance.”  I imagine others might find the flare interesting. 

I wanted to compare this vintage Olympus lens to a fast modern lens of similar focal length; I chose the Sigma 105mm F1.4 DG HSM Art (JP2019-144477_Example01P)  .  It’s focal length is similar and it reaches the f/2 aperture as the vintage Olympus lens.  Pricing is similar, too; B&H lists the Sigma at $1500.  The Sigma lens is not only faster, it also is capable of much closer macro performance.  These added capabilities offer some justification for its larger size. The vintage Olympus is 127mm long, 50mm dia, 520g; the new Sigma is 172mm long, 105mm dia, 1600g.  The vintage Olympus also uses far fewer lens elements; 7 for the vintage Olympus vs. 16 for the new Sigma.

Reviewers of the Sigma lens describe it in ways that sound similar to reviews of vintage lenses.  Some concentrate on its size, with a lot of snarky comments. They all agree on its excellent build quality and bokeh, agreeing with Sigma’s claim that his lens is a “Bokeh master.”  I found one site’s description a little baffling from an engineering point of view:  “The colors from the Sigma 105mm f1.4 DG HSM Art lens are interesting for sure. They’re nice, but they’re muted as if Sigma really designed this lens for portraiture. Certain tonalities are pretty vivid, but those most attributed to skin color are more muted.”  All reviewers noted that the lens is quite large, limiting its applications.”  If you know how to evaluate such properties in Zemax, let me know.

Photos and schematics of the classic Olympus lens (left) and the modern Sigma lens (right.)  The Sigma lens is obviously bulkier.

To fairly compare the two lenses in Zemax, I first converted to real glass types, where all glasses in the patent disclosures found good matches in the glass catalogs.  I also compared only at f/3, which seems fairly fast yet still far enough from the Olympus’s maximum aperture that it should represent the lens fairly. 

Lateral color, defined as the spread of F, d, C lines, is significantly lower for the new Sigma lens than the vintage Olympus.  Note that the Sigma lens’s 2X advantage in lateral color corresponds to a 4X advantage in pixel count, if no fringing is desired.

Distortion of both lenses is small.  I suspect that the small advantage here for the vintage Olympus is unimportant.

Nominal MTF for both lenses is excellent.  I suspect that as-built MTF would be indistinguishable.

Vignetting is good for both lenses.  I suspect the lower falloff for the Sigma would be noticeable.  

A crude way to evaluate Bokeh is to look at spot diagrams for out-of-focus spots.  Below, I set the camera to best focus for a 3m object distance, then evaluate the spot diagrams for an object at 10m.  The bokeh on both lenses looks very good; the spots are round and even.  At full field, the spots on the vintage Olympus lens show some departure from circular, representing some loss of bokeh quality.  Sigma Bokeh looks much better.  Note that this analysis omits an importont source of bokeh degradation for the Sigma lens - the aspheric surfaces.  Mid spatial frequency errors in surface form are known to cause unattractive modulations in bokeh; showing such effects in Zemax is beyond the scope of this simple post.

Conclusion:  Both lenss seem really good.  Preference for vintage Olympus might be justified by lens flare or vignetting.  size, physical feel  Convenience of new Sigma lens (metadata, autofocus, internal focusing, etc.) would be a big counterbalance for many users.

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.

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

        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

Design files