Photographic lenses - prime

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 glass types that aren’t included in any current glass catalog, yet the test 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.

         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), 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 also 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.

    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 t 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.

    The exercise led to several interesting models:

- super telephoto, super low f/#

- evolution of 50mm

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.  Then 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 smartphone 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 catadiprtric designs.

September 14, 2016 -  19 fisheye lenses posted

              Today I posted 19 lens files for fisheye lenses.  Modeling these lenses presents special challenges - 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 rational 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. 

        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.

    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.

Listing of design files: