January 4, 2024- 109 models of microscope objectives, chosen from Yueqian Zhang’s library

Today’s posting of 109 models is based on work from Yueqian Zhang.  This work is nicely summarized in a 2017 IODC paper, “Systematic design of microscopic lenses.”  More detail is presented in a series of three papers in the journal Advanced Optical Technologies, and even more detail in his doctoral dissertation at Friedrich Schiller University Jena, Germany.

Taken together, this work is the ideal of using a large lens design library to illuminate design principles and trends, thereby pointing towards new designs.  Dr. Zhang  didn’t use the library on this site; he built his own.  However, his work represents exactly the kind of understanding that motivates me to build this website.  Dr. Zhang describes the wide goals of his work eloquently, to “subtract the hidden assumptions to reach the reality.”

Dr. Zhang’s IODC paper begins with a quick summary of the development of the microscope objective, highlighting the designs from Lister & Amici.  He shows that modern microscope objectives contain three distinct groups of lens elements:

- The first group, closest to the sample, must collect light from a very large numerical aperture.  To accomplish this task without introducing too much spherical aberration, this group often includes a hemispherical lens closest to the sample, as well as several thick quasi-aplanatic meniscus lenses.  Chromatic aberration correction is also important within this group, requiring tightly constrained glass choices.

- The second, middle group, is described by Zhang as being “composed of several cemented doublets and triplets, providing great contribution to spherical aberration, coma, axial chromatic aberration and especially zonal error and spherochromatism correction. For most of the sophisticated systems, the middle group consists of 6-10 elements with different cementing setups.”

- Finally, the third group, farthest from the sample, “is helpful for controlling Petzval curvature, as well some residual error from the front and middle groups.  It often consists of thick meniscus lenses or a symmetrical triplet.”

Zhang eloquently shows how these three groups can be constructed from increasingly-complex building blocks to migrate the three-group concept from a simple design to a modern, high-performance design.  I particularly liked his description of how designs can control higher-order spherical aberration using Merte surfaces – steeply curved, cemented surfaces with small index change but large dispersion change.  (For completeness, I added Merte’s US patent #1,467,804 to the Photo Primes page.  I find it interesting that Merte’s patent doesn’t claim or describe its essence: a small index difference and a large dispersion difference.) 

Zhang then uses this insight to demonstrate a systematic design process, generating a complex 11-element 40X 0.85NA objective from a simple 4-element 10X 0.25NA textbook starting point

All of this insight was developed, in part, via a large collection of lens design models.  Zhang’s  database includes 484 models, pulled from patents in Japan, Germany, and the US.  The models mostly focus on the field of biomedical research and semiconductor industry - optical disk objectives and in vivo endoscopic microscope objectives are excluded.  Zhang includes diffractive surfaces in his analysis, but I excluded them from the models I built.

Zhang notes the rate of patent activity is  not at all uniform.  It’s sparse before the mid 60’s.  “From 1965 to 1975, most of the basic objective structures were invented for biomedical and metallurgical applications… Microscopes with infinity optics then became the major type from 1980s. The second peak period started from the mid-1980s, following the flourishing demand of the semiconductor industry…  The second peak period started from the mid-1980s, following the flourishing demand of the semiconductor industry. The working distance and corrected spectral range were extended during this period,… applying fluorescence microscopy to biology and material science led to a revolution of objective design for research application… The highest peak period of microscope objective publication was found around 2000”

Zhang also noted the distribution of the assignees for the patents: Olympus & Nikon together own 75% of the patents.  Zeiss, Leica, American Optical, & Mitutoyo each have 5-8%.

This short summary of Dr. Zhang’s work doesn’t begin to express the insights and richness of his work.  All serious students of lens design should read his IODC paper, his series of papers (I, II, & III) in Advanced Optical Technologies, and even his dissertation

. Sadly, Dr. Zhang was unable to share his model library with us.  I built a subset of the library with the help of Bill Claff, of www.photonstophotos.net/ .  Bill started with the patent listing from Dr. Zhang’s dissertation.  He very efficiently turned the design listings in the patents into basic Zemax files; these files are available on his website with all patented embodiments, not just the subset collected here.  Making these files helpful reference points for optical engineers required several steps.  These steps were often tricky.  Because excellent correction of chromatic aberration is necessary for the objectives, I turned the disclosed material index & dispersion into real glass models.  I also tried to make sense of the disclosed cover glasses, image distances, and conjugate distances, all to find diffraction-limited performance on-axis.  After establishing excellent performance axially, I found the pupil position by forcing telecentricity.  I established field and image sizes by choosing points where the design seems to fall apart.  In these steps, I diverge a little from Dr. Zhang’s approach; he kept standard distances and the disclosed paraxial properties, but he tweaked the prescriptions a bit to get diffraction-limited performance. Challenges with this process include 1) use of obsolete glass types, 2) unclear disclosure of cover glass thickness and material, 3) unclear disclosure of immersion fluid, 4) unclear disclosure of conjugate distances, and 5) errors in the disclosed design prescriptions.

A good example of a challenging design to convert from the disclosure to a working Zemax file is the first example of US Pat. Appl 20030043473.  The model built directly from the disclosure gave rather poor performance, despite my searching for good combinations of cover glass thickness and index, possible immersion fluids, and optimization of conjugate distances.  While troubleshooting the design, I noticed a problem with surface 13; the disclosure calls for nd = 1.6968, Vd = 51.352, which is a marginally poor match for catalog glasses.  By luck, I noticed the Abbe value is an exact match for a nearby glass.  (Further complicating matters, the index and Abbe number for this other surface is a good match for Schott KF9; but Dr. Zhang tells me that the actual glass is an unknown Hikari glass with special partial dispersion.)  Optimizing n & V on surface 13 yields excellent performance for nd = 1.6968, Vd = 55.41, a close match for Schott N-LAK14.  This glass has a close match to the disclosed index, but is far from the disclosed Abbe number.  I wonder how such an error could occur.  Maybe someone accidentally transcribed the Abbe number from surface 17 onto surface 13.  Such transcription errors would be understandable in 1981, when manual transcription was common; but this application was filed in 2001, when the patent process was primarily digital.  In the end, the application was abandoned.  Hopefully this error would have been corrected before patent issuance.  Such patent transcription errors can be important in IP law; recent patent litigation between Immervision and LG provides a good example, in which an aspheric table from one example design was incorrectly assigned to another.

Finally, I made a small attempt to expand on Zhang’s comprehensive work by examining the overall distribution of glass types used in the designs.  The figure below shows that five glass types dominate the glass usage in microscope objectives.  Together, these five glasses comprise 30% of the disclosed glass elements, neglecting plano-plano elements such as cover glasses and filters. Calcium Fluoride and S-FPL53 are clearly chosen for their low dispersion.  GFK70 is helpful in correcting color because it lies far from the standard line in partial dispersion.  (I find it interesting that it’s the only commonly-used glass that has a good match to the Sumita catalog, but no other catalogs.)  N-KZFS11, a short flint,  has low index and low Abbe number, making it a good companion for Merte surfaces for many other glass types, including CaF2.  N-LASF31A and S-LAH58 have relatively low dispersion for such a high index.

#     nd  Vd  Sample glass           Rel price

191 1.44 95  CaF2, S-FPL53      53

102 1.49 82  S-FPL51, N-PK52A, 11

68  1.61 44  S-NBM51, N-KZFS4 7

53  1.64 42  N-KZFS11,               30

39  1.88 41  N-LASF31A, S-LAH58 37

35  1.57 71  GFK70

I compared this list of commonly-used glass types to the list of commonly-used glass types for photographic telephoto lenses, shown on the Primes page.  None of the glasses are common between the two lists.  Part of the reason for this mismatch may be that the raw material cost is a much smaller portion of the product cost for microscope objectives.  None of the common telephoto glasses has a relative price over 10; at least four of the common microscope glasses have a relative price over 30.

February 7, 2021 - 15 designs posted from Braat & Török's Imaging Optics

Joseph Braat kindly provided some explanatory text:

"Example 7.59a is an achromatic Lister objective from 1830 (Imaging Optics, page 501, f =16 mm, NA=0.25, field diameter 600 um). The objective is comprised of a classical achromatic doublet and a closely resembling scaled copy of it, used at a different magnification. By an experimental study of the aberrational behaviour of a cemented doublet as a function of its lateral magnification, J. Lister devised the optimum combination of two doublets such that spherical aberration and coma of each doublet are cancelled by the contributions of the other. Lister used the typical crown and flint glasses of his epoch, well represented by the present-day Schott SK11 and F2 glasses.   Colour correction is achieved for the standard achromatic range of 486 < λ  < 656 nm     

"Example 7.59b is an achromatic Amici-type objective, proposed and constructed by him around 1840 (Imaging Optics, page 501, f =6 mm, NA=0.65, field diameter 250 um). The field is slightly curved which was not perceived as a limitation for visual observation. The performance of the objective with respect to monochromatic aberration and axial/lateral chromatic aberration is not entirely at the diffraction-limited standard for present-day microscopy.            

"Example 11_40_US6504653 is an achromatic immersion objective of the Amici-type, patented by Carl Zeiss Jena (2002), Imaging Optics, page 849). The specifications are:  f =4.7 mm, NA=1.40, field diameter 140 um, wavelength range: 435 nm <  λ < 690 nm. The performance of the objective with respect to axial/lateral chromatic aberration is not at the diffraction-limited standard for present-day microscopy. Especially the axial chromatic aberration (of the order of 1.5 um) largely exceeds the Rayleigh focal depth (0.19 um at the central wavelength of 550 nm). These shortcomings are due to the special requirements for this objective to be used in fluorescence microscopy with illumination through the very outer parts of the aperture (beyond NA=1.3).

"Example 11_40_optimised is an apochromatic immersion objective of the Amici-type (see Imaging Optics, page 849 for the original US patent version), with an improved imaging performance as compared to the patent embodiment. The specifications of the objective are:  f =3.83 mm, NA=1.30, field diameter 140 um, wavelength range: 420 nm < λ  < 690 nm. The performance of the objective with respect to axial chromatic aberration is such that that the chromatic excursion over the entire wavelength range (0.28 um) is definitely less than two Rayleigh focal depths (one Rayleigh focal depth equals 0.19 um at the central wavelength of 550 nm). The total lateral chromatic excursion at the rim of the image field is less than 60% of the half-width of the perfect Airy disc. This design closely resembles the dry high-NA objective of Fig. 7.62 in the book Imaging Optics, designed by the first author in the 1980s using several Schott glasses with abnormal partial dispersion that have been discontinued in the 1990s for environmental reasons.

"Design 7.64 is a monochromatic four-element objective (Imaging Optics, page 505), using spherical surfaces with the following specifications:  f =9.2 mm, NA=0.40, field diameter 1.0 mm, wavelength λ  = 633 nm (He-Ne laser). The objective has been used in the Video Long Play system, VLP, with large-diameter substrates (30 cm). The only significant aberration is field curvature. An important specification of scanning objectives for optical disc systems is the ‘free working distance’ (FWD), the distance between the last surface of the objective and the top surface of the optical disc. In this example the FWD is equal to 4.2 mm (disc material is a PMMA-type plastic).  

"Design 7.67 is a single element objective for the CD-system (Imaging Optics, page 509), with one flat and one aspherical surface, operating at the infrared wavelength of 785 nm. The aspheric surface has been replicated on the best -fit spherical surface of the convex-plano lens body from an aspheric mould with the aid of a UV-hardening lacquer, allowing mass production. The specifications of the lens are:  f =4.5 mm, NA=0.45, field diameter 240 um, FWD = 1.8 mm, polycarbonate disc substrate with a thickness of 1.2 mm, central wavelength  λ = 785 nm (AlGaAs laser). The laser has a small spectral width of typically  +-0.1 nm due to multimode operation and a possible shift of the same amount due to fabrication spread and temperature drift of the semiconductor laser source. In the Zemax-file the refractive index of the UV-lacquer material has been defined by its nd – Vd  values  (1.569432, 34.557). The Schott dispersion coefficients of this material are given by  A0 = 2.438286800E+000, A1 = -2.297557500E-002, A2 = -1.069041000E-002, A3 = 1.053833500E-002,  A4 = -1.166543600E-003, A5 =  3.309457900E-005. 

"Examples 7.68a, 7.68b and 7.68c (Imaging Optics, page 510), illustrate the various designs that are possible when a bi-aspheric single lens is used as scanning objective. The lens material is made of a mouldable plastic material (n=1.53) and both surfaces are made aspherical such that an aplanatic design can be realised. The lens specifications are f =4.5 mm, NA=0.45, polycarbonate disc substrate with a thickness of 1.2 mm, central laser wavelength  λ = 785 nm. 

"Example 7.68a is a lens which shows a resemblance with an inverse telephoto camera lens and allows for a large free working distance of 2.9 mm (Imaging Optics, page 510),. The specifications of the lens are:  f =4.5 mm, NA=0.45, lens refractive index is 1.50, field diameter 400 um (slightly curved field),  λ = 785 nm (CD-system). The useful field diameter for a microscope objective in an optical disc system is determined by the maximum allowable wavefront aberration: half the diffraction limit or 0.035 λ   rms wavefront aberration. The first lens surface is highly aspheric and is situated close to the paraxial centre of curvature of the second lens surface. This geometry explains the large field, in an identical way as in the Schmidt telescope with its aspheric corrector plate.

"Example 7.68b is a lens with a telephoto behaviour (Imaging Optics, page 510), and has consequently a small free working distance (mechanically 1.10 mm). The lens specifications are f =4.5 mm, NA=0.45, refractive index 1.50, λ  = 785 nm (CD-system). The flat field has a diameter of  400 um. Both lens surfaces show a large departure from the best fit sphere and need many (even) aspheric coefficients to accurately describe this departure (up to the 26th  power of the lateral surface coordinate for an accuracy of 0.001 λ in the outgoing wavefronts).     

"Example 7.68c is a more standard biconvex aspheric lens (Imaging Optics, page 510), with an average free working distance of 1.33 mm. The lens specifications are f =4.5 mm, NA=0.45, refractive index 1.53,  λ = 785 nm (CD-system). The slightly curved field has a diameter of  300 um. The aspheric departures of both lens surfaces have a much reduced departure from the best fit spheres as compared to the examples 7.68a and 7.68b (coefficients up to the 10th  power of the lateral surface coordinate are needed to specify the outgoing wavefronts of the lens down to an accuracy of 0.0002 λ ). A tolerance analysis of the three designs shows that the examples 7.68a and 7.68b show virtually unfeasibly small values for mass-fabrication. Design 7.68c has been optimised with respect to mechanical and material tolerances; distances have to be maintained within a 0.01 mm range, angular deviations to typically 1 mrad, refractive index variations to within 0.001 and temperature drift to ± 30deg C. Several tolerances of the designs 7.68a and 7.68b are more tight by at least a factor of 10 than those of design 7.68c.

"Example 7.70 is a ‘buried’ reflective microscope objective (Imaging Optics, page 513), based on the Schwarzschild reflective design. The surface of the small primary mirror has been made aspheric allowing for a design with zero spherical aberration and small comatic aberration. The free working distance is 1.59 mm. The objective specifications are f =0.84 mm, NA=0.45, refractive index lens body 1.51 (glass BK7),  λ = 785 nm (CD system). In contrast with all preceding objective designs for optical disc systems that had a large finite conjugate distance at the object side, this objective has finite conjugates and operates at a magnification of  -4.5. The slightly curved field has a diameter of 150 um (in angular measure 2x10 deg at the object side).

"Example 7.73c is a biconvex lens with two aspheric surfaces for the DVD system (Imaging Optics, page 517). The lens specifications are f =3.3 mm, NA=0.60, refractive index 1.53, λ = 650 nm, polycarbonate disc substrate with a (one-sided) thickness of 0.6 mm. The slightly curved field has a diameter of 160 um (the Rayleigh focal depth of the DVD system is 0.8 um).

"Example 7.75a is a biconvex lens with two aspheric surfaces for the Blu-ray system (Imaging Optics, page 518). The lens specifications are f =1.75 mm, NA=0.85, refractive index of the lens material is  1.68 (moulding of glass),  λ= 405 nm, polycarbonate disc cover layer of 0.1 mm. The slightly curved field has a diameter of 50 um; at the rim of the field, the field curvature is one focal depth (the Rayleigh focal depth of the Blu-ray system is 0.21 um). The bi-aspheric lens has extremely tight manufacturing tolerances and cannot be mass-produced.             

"Example 7.75b is a two-element option for a Blu-ray objective in which each element has been provided with one aspheric surface (Imaging Optics, page 518). The lens specifications are f =1.75 mm, NA=0.85, lens body material is the Schott FK5 glass (refractive index 1.499),  λ = 405 nm, polycarbonate disc cover layer of 0.1 mm. The curved field has a diameter of 200 um. At the rim of the large field, the field curvature equals 12 focal depths (the Rayleigh focal depth of the Blu-ray system is 0.21 um). The manufacturing tolerances of the lens system are such that mass-production is feasible. 

February 10, 2017 - 9 designs posted

    Includes three reflective designs, three immersions, and one low-magnification inspection scope.

January 21, 2015 - 25 designs posted

    When I started collecting these files, I had in mind the objectives for typical upright microscopes, objectives like the 40X one in US04379623-1.  I’ve used this kind of file for baseline designs in various proposals and other concept development tasks.  I added other design types more out of curiosity.  Notable designs include: low magnification inspection microscope (US04501474-1) several immersion objectives with super-high NA (US05532878-1, US08199408-1), and some intriguing catadioptric designs, also with very high NA (US07633675-1).  Most of the models include only the objective, but some, such as US07158310-6, include the field lens, too.

    If you find these files interesting or helpful, please contact me via e-mail or the comments section.  Even better, please join the collaboration by contributing some of your own design files.

Summary of designs

Design files