502-14 Relays and Microscopes

OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-2 14-1 is inverted and reverted. For many many For reverted. and inverted is Porro-Abbe System Pechan-Roof Abbe-Köenig nd binoculars, it is important binoculars, it is important that image nd the image erection method must be added to the to added be must method erection image Section 14 Relays and Microscopes Relay systems Relay telescope system. Methods: Prisms Porro System The image by a KeplerianThe image produced telescope the same has orientation An as the object. applications, such as terrestrial telescopes a Image Erection Image OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp z 14-4 14-3 XP EYE z f XP FIELD f EYE f FIELD f L = 4a Prism 1 Prism 2 modeled modeled as a plane parallel glass. plate of st be sized so that entrance the and exit faces m faces to the length of the tunnel diagram. the tunnel diagram. m of faces to the length or binoculars or is usually placed between the a clude the tunnel diagram erecting the clude the tunnel diagram prism of the intermediate image plane. image intermediate the intermediate image size. The prism dimensions are dimensions prism The size. image intermediate a OBJ f a OBJ OBJ f f Refraction at the surfacesparallel the plane of the prism plate of model be included must as well as the accompanying of shift Telescope layout: Telescope The telescope layout is now modified to in to modified now is telescope layout The vignette any prism) therefore tunnel diagram sized as to not (and the must system. The be rays foror the specified FOV determined. The erecting prism The erecting prism a Keplerianin telescope objective intermediate the lens and image. It mu do not vignette the FOV. To minimize minimize is usually the prism as small To weight, as possible. the FOV. vignette not do tunnel diagram prism to be The prism allows the The prism geometry relates the pris sizes the of common PorroConsider the System: Prism Specification Prism Prism Specification Prism OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp   14-6 14-5 z n 1    1  n 1    XP 1    EYE  f  UC     n L/n = 4a/n  FIELD C n 1 f     45 sin sin  1      sin a 45 45 sin NA n      U C At the TIR limit: limit: TIR the At  The top ray will lose TIR before the bottom TIR before the bottom ray The top will lose limit. therefore defines the NA and ray Limiting NALimiting sin sin 45 sin is limited Total is limited loss of Internal the by image plane. An air-equivalent prism is prism air-equivalent An plane. image termined termined from the size of the reduced tunnel º  U   º '    ' L = 4a n  L    n  sin in air  sin sin OBJ f NA a   The fastest f/# or NA that a prism that a prism will The fastest or NA support f/# Reflection at the hypotenuse of the prism. the prism. of Reflection at the hypotenuse right in air: angle prism a Consider The reduced tunnel diagram can be used to simply simply determine to can be used tunnel diagram sizes the prism reduced The without refracting the rays or shifting the intermediate unvignetted. the rays diagram are is sized that all reduced tunnel so of The used. TIR Limit TIR Limit in Prism Systems Prism Specification – Specification Prism Diagram Tunnel Reduced The physical size of the prism de then be the prism physical can The size of diagram on the schematic. OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-8 14-7 F2 BaK4 index n index index n index BK7 1.45 1.5 1.55 1.6 1.65 1.7 1.45 1.5 1.55 1.6 1.65 1.7 8 6 4 2 0

8 6 4 2 0 16 14 12 10

16 14 12 10 Limiting f/# Limiting Limiting f/# Limiting TIR because the resulting compound angles the resulting TIR because compound n 1    1 nn 11      11  ll of these glasses (transmission, (transmission, these glasses stria, etc.) are all excellent. ll of 2 Limiting f/# Limiting      nn        2 n 2 1 n 1 n        n    211 2 2    2 Limiting NA Limiting 211 n 2        Limiting f/# Limiting NALimiting sin sin 45 sin Limiting NALimiting sin 45 cosLimiting NA sin cos45 1 sinLimiting NA sin Limiting f/# 1 1 If the objective lens is faster the than the of edge the from rays f/#, limiting pupil will not experience TIR. For fast must glass index objective lenses, higher be used. increase the angle of incidence beyond the critical incidence increase beyond the angle of angle. BK7 prisms prisms BK7 are in older found designs and lower cost systems. Note that the optical quality a of surfaces Roof do not experience this loss of BK7BaK4 n = 1.517F2 n = 1.569 n = 1.620 5.02 3.38 2.56 TIR Limit TIR Limit – Choice Glass TIR Limit TIR Limit in Prism Systems OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-9 14-10 z EYE OBJ f Objective Eye Lens Eye  R R z zf EYE f image formed by the by formed image  2 h RK  R z  e MP of the original the original Keplerian of telescope. e MP is positive. The system MP equals the The system MP is positive. MP m MP Eye Eye image. The second intermediate image is image intermediate second The image. there will be some to there due will some light in the pupil be Lenses e objective and the eye lens of the Keplerian e objective the eye lens of and The intermediate intermediate The the binoculars is faster than the TIR limit, binoculars the is faster than the TIR limit, Systems Nominal ece. The re-imaging causes an image rotation image an causes re-imaging The ece. R Exit Pupils Exit Porro Prism z Relay Lens Relay 1 h R R  z z a Porro Prism a Porro Prism system will the XP. clip a different side of  OBJ f R m Objective Objective The net MP of the relayed of Keplerian telescope MP The net th the relay and of the magnification of product Fresnel reflections. Fresnel intermediate objective a second is relayed to the eyepi placed at the front focal point of of 180°, correcting the image orientation. The final XP becomes squared-off. becomes final XP The pupil where TIR is lost, the In the regions of relay A or erecting lens inserted between th telescope can correct the image orientation. At each reflection, the loss of TIR will clip an edge of the XP. At each reflection, the XP. TIR will of clip an edge the loss of reflections the four Each of in The Porro Prism erecting system in a pair of binoculars can be thought of as four right right as four of thought Prism binoculars can be erecting Porro of The system in a pair If objective in the angle prisms. lens used are clipped. the XP of portions TIR Limit Limit –TIR Exit Pupil Effect on Relay or Erecting Lens Erecting or Relay OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp z 14-11 14-12 z XP XP ER ER Eye Lens Eye Lens create the exit pupil ture, transferring the intermediate intermediate pupil is Marginal Ray EYE EYE f f   larger than this image, than this image, all larger er to the exit pupil with the at the front focal point of the eyepiece. the eyepiece. at focal point of the front re into the relay aper to the relay the relay to lens. An Relay Relay aller than the relay lens diameter. A relay tive) are mounted in the same tube and have and tube same the in mounted are tive) with the eye, the eye, the final field with will not lens e pupil into the following relay relay All of into the following lens. e pupil image to the second intermediate image. image. intermediate second the to image by the objective transferred will be to the pupil into image image into pupil space to rred down the optical system. the optical rred final field system. The down shown could be used. However in many be used. could shown in However many e second field lens and the eye lens. Field Field Field Field near the intermediate near the intermediate images. common A If the relay lens diameter is into the eye lens, rath but OBJ OBJ f f Objective Objective entrance the relay pupil to lens. object point collected the light from an of second image. For an optical system used image image the relay lens aperture appropriate eye relief. appropriate eye The first field lens images The first field lens images the objective apertu The eyepiece also images The eyepiece also images the intermediate and the eye relief. In this example, the intermediate is sm pupil objec the (except lenses the situations, all of diameters. same the approximately located at the relay lens. relay The lens images the first intermediate located be must image intermediate second This th The eyepiece combination is the of diameter lens with a smaller that than The first field lens images The first field lens images the objective/stop in Field lenses can also be added at or at or added Field lenses also be can arrangement image is for each field lens to th the light collected the objective by is transfe the eyepiece. lens is part of Relay Lenses and Field Lenses and Relay Lenses Ray Bundle with Relay and Field Lenses Relay Lenses with Bundle Ray OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp z z 14-14 14-13 z Image Image Relayed Relayed Pupil Image Relayed Intermediate is located pupil at the Intermediate Pupil Intermediate Pupil and Glareand Stop Pupil XP of the telescope. The ER Relay Lens Relay Relay Lens Relay Image Relay Lens Relay an the focal length of the relay the relay lens, the glare length of the focal an termediate termediate size. Since the focal length pupil t intermediate image, but the stray light is light stray the but image, intermediate t Intermediate the glare stop is also known as a Lyot is also known the glare stop In Stop. the eyepiece. at the frontof focal point is cooled to reduce unwanted thermal thermal radiation. reduce to unwanted is cooled image, the relay erecting or lens also stem stem can scatter outside the FOV from in the image, the intermediate the image, rmediate rmediate to serve as a glare for pupil stop The stray light is blocked by the glare the glare stop. by stray light is blocked The Field Lens diameter diameter relay erecting or is required. lens ture can serve the glare as stop. The eyepiece (field lens and eye lens) projects the relayed projects the eye lens) eyepiece and (field lens The s intermediate the to the pupil Objective Objective Reflected/Stray Light Reflected/Stray Objective/Stop If the first field lens is not used, a larger a larger If the first used, field lens is not Of course, the relayed image must be located be must relayed image the course, Of A physical physical aperture A placed can be at the inte sy scattered stray entering or the light. Light the telescope system as from (such barrel). In In addition to creating an second intermediate the telescope is of is changed. produces an intermediate intermediate produces an pupil. transfer and infinity to image blocked before the relayed image image the relayed before is formed. blocked certain In applications (especially astronomy) relay the relay lens, and lens aper of the objective lens is typically the objective of lens is typically th longer much located the rear is then stop just outside the relay offocal point lens. The stray the firs light will be superimposed on infrared systems, as it it is called Stop a Cold at the first If a field lens is used intermediate The The glare should be the stop same size as the in Glare Stop Relay or Erecting Lens and Pupils and Lens Erecting or Relay Without field lens at a the Without image, intermediate first the relay lens produces the intermediate pupil. With a field lens at the at field lens a With image, intermediate first the intermediate is pupil at the relay lens. 14-15 OPTI-502Optical Designand Instrumentation I

In many systems, the relay works at approximately 1:1 conjugates or magnification. The object distance for the relay lens is then twice the focal length of the relay lens. This situation limits the FOV of the system and/or requires a large diameter relay lens.

The FOV is limited by vignetting at the relay lens.

Relay Lens Objective

f 2f Objective Relay 2fRelay

A field stop and a glare stop can be added to this system. The glare stop would be located where the chief ray crosses the axis following the relay lens.

Since the FOV is small, adding a field lens at the first intermediate image plane may only provide a moderate increase in the FOV of the system.

14-16 OPTI-502Optical Designand Instrumentation I

Increased FOV can be obtained by using an erecting couplet. The single relay lens is split into a pair of elements that provide the 1:1 imaging for the relayed image.

Since the distance between the first intermediate image and the first element of the couplet is the focal length of one of the relay elements, the cone of light from the intermediate image has less distance to expand. A significantly larger intermediate image and FOV is supported.

The FOV is still limited by vignetting at the relay lens.

Objective

fObjective fRelay 2fRelay fRelay

Erecting or Relay Couplet

The erecting couplet shown has the same diameter as the single relay lens of the previous slide. 14-17 OPTI-502Optical Designand Instrumentation I

An intermediate pupil is formed between the two relay elements, and a glare stop may be placed at this location. The second relay element will produce a virtual image of the intermediate pupil that is reimaged by the eyepiece to produce the exit pupil and eye relief.

The common configuration is for the two elements to be separated by twice the focal length of a single element. Note that the system length has not changed as the separation between the two intermediate images remains 4f Relay . The magnification provided by the erecting couplet is independent of the relay element separation. Changing this separation will change the distance between the intermediate pupil (glare stop) and the second relay element which moves the location of the final intermediate pupil produced by the erecting couplet. Varying this separation allows the location of the exit pupil to be adjusted to produce the desired value for the eye relief.

Glare Stop Objective

fObjective fRelay 2fRelay fRelay

Erecting or Relay Couplet

14-18 OPTI-502Optical Designand Instrumentation I

Multiple relay lenses can be used to transfer the image over a long distance. Examples include periscopes, endoscopes and borescopes.

Objective FieldRelay Field Relay Field

f OBJ ABCDE

The image is transferred from field lens to field lens: Lens A images the objective aperture into Lens B Lens B images Lens A into Lens C Lens C images Lens B into Lens D, etc. The entrance pupil is imaged into each relay lens, and the image passes through without vignetting. There is no light loss except for transmission losses.

Starting with Lens B, a series of 1:1 imaging systems is often used. All of the lenses will have the same focal length and diameter. The relay system is completed with an eye lens or eyepiece. The final image can also be placed on an detector array. 14-19 OPTI-502Optical Designand Instrumentation I

September 25, 1608

Hans Lipperhay was provided a letter of introduction in order to present his invention to the States-General in The Hague of the Netherlands for the purpose of obtaining a patent:

“a certain device by means of which all things at a very great distance can be seen as if they were nearby, by looking through glasses…”

1608: Dutch (or Galilean) Telescope

Lipperhay 1570-1619, German-Dutch fOBJ fEYE

tfOBJ f EYE • Erect image • Usually a low magnification • Often short and compact • Small field of view

14-20 OPTI-502Optical Designand Instrumentation I

October 2, 1608

Hans Lipperhay receives a request from the States-General “to ascertain … whether he could improve it so that one could look through it with both eyes.”

October 4, 1608

Committee is formed “for the purpose of examining and trying the instrument in question on the tower of the quarters of His Excellency” and “to negotiate with the inventor about the fabrication, within one year, of six such instruments made of rock crystal.”

December 15, 1608

Members of the committee report “that they have seen the instrument for seeing far with two eyes, invented by the spectacle-maker Lipperhay, and have found the same to be good.”

However, “since it is evident that several others have the knowledge of the invention for seeing far, the requested patent be denied the petitioner,…”

It is interesting to note that the development of binoculars began almost concurrently with the development of the telescope. 14-21 OPTI-502Optical Designand Instrumentation I

Galileo Galilei used a long high-magnification version of this design for his famous astronomical observations.

Galileo produced his first telescopes in 1609 (3-10X) with later improved telescopes with magnifications up to 20-30X. In 1610, he published his observations on the moon, the moons of Jupiter and the constellations and the Milky Way (Starry Messenger). Other observations included the rings of Saturn, the phases of Venus and sunspots.

This 21X telescope from 1609-10 has a plano-convex objective lens with diameter of 37 mm, an aperture of 15 mm, and a focal length of 980 mm. The telescope is 927 mm long with a field of view of 15 arc min. Galileo; 1564-1642, Italian

14-22 OPTI-502Optical Designand Instrumentation I

1611: Astronomical (or Keplerian) Telescope

Proposed by Johannes Kepler in 1611 Christoph Scheiner constructs first Keplerian telescope in 1617

• Inverted Image • Higher magnification • Longer length • Good field of view

Kepler; 1571-1630, German

fOBJ fEYE

tf OBJ f EYE

14-24 OPTI-502Optical Designand Instrumentation I

Circa 1635: Christoph Scheiner introduces a single erecting lens to produce an erect image.

Scheiner Erecting System or “Two-Lens Eyepiece”

The field of view is limited by the diameter of the erecting lens.

Scheiner; 1573-1650, German-Austrian

Exit Pupil

fObjective 2f Relay 2fRelay fEye Objective Erecting or Relay Lens Eye Lens OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-26 14-25 Exit Exit Pupil Pupil Eye Lens Eye Eye f f Stop Field Stop Field Eye Piece Eye Relay f Field Lens first intermediate first intermediate image Huygens; 1629-1695, Dutch 1629-1695, Huygens; Relay Relay Stop Stop Glare Glare 2f 2f used a two element used a two element erecting couplet to Erecting or Relay Couplet or Relay Erecting Relay Relay serted at or near the f f an erect image and acceptable magnification and between the two erector two lenses. between the em em or “Four-Lens Eyepiece” Objective Objective f or “Three-Lens Eyepiece” f Objective Objective Coupletor Relay Erecting Lens Eye field of view. field of System Schyrle Erecting a glare Note the presence stop of lens eyepiece invents the two Christian Huygens 1662: incorporating both an eye lens and a field lens. Schyrle-Huygens Erecting Syst produce a practical produce a terrestrial telescope with 1645: Anton Maria Maria de Rheita (1604-1660) Schyrle Anton 1645: A Brief History A Brief History of the Telescope A Brief History A Brief History of the Telescope In some telescopes, In some additional an field lens was in five-lens eyepiece. a resulting in OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-28 14-27 z XP EYE ER mm EYE f EYE f 250  h use in the late 1600s, however in the late use 1600s,  mm EYE Eyepiece MP Eyepiece 250 MP is negative).  O OEYE O z zf z strial refracting telescope was firmly in firmly was telescope refracting strial not intended for astronomical astronomical intended for but for not use, st notably the achromatic objective in the e lateral e lateral objective and magnification the of Image of h OTL of objective an plus an eyepiece or ocular. O  z  O O z z    V OBJ EYE F mmMP the four-lens eyepiece in was OBJ m OBJ f O Objective z h Note that the visual magnification Note that the visual magnification is negative ( The visual magnification th of visual magnification The is the product the MP of the eyepiece. of the MP The compound microscope microscope a sophisticated is magnifier enlarged presents image compound an The which of nearby object to the eye. It consists A Brief History A Brief History of the Telescope Microscopes There is some that evidence some There is place by this time. time. this place by the mid-1700s. in tubes also began brass of use The were telescopes of produced vast majority The military nautical and purposes. mid-1700s, the modern design form of the terre the of form design modern the mid-1700s, it fell out of favor until the mid-1700s. mo there were improvements follow, While to OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp z 14-30 14-29 WD Stop  10X 0.10 F 

OBJ

f sin OO Height Shoulder  O NA n Objective z m  O   E  F f z defined as the distance from as the distance definedrear from the focal 215 mm. 215 mm. A relaxed eye (image at infinity) mm int of the eyepiece (intermediate image). 250 stance from the object to the object to the stance from OBJ tives are interchanged with a tives are interchanged with f OTL OBJ EYE ff s magnification s magnification but remains in ective and the end of the tube ed. Objectives and eyepieces OTL tion corrected assuming a cover a tion corrected assuming   e objective magnification, e objective magnification, V OBJ m m The NA of a microscope a microscope of objective in definedis The NA object space the half-angle by the accepted of input Along with th ray bundle. the NA is inscribed the objective is inscribed on barrel. the NA telecentric Microscope object objectives are often in is placed The stop at the rear focal point of space. not does the objective that the magnification so change with object defocus. The working distance WD is the di distance The working WD first element 1the objective; of can be less than mm for high- objectives. power The mechanical tube length is separation the shoulder between the obj of the threaded mount of the eyepiece into which is insert must be used at their design conjugates and are not necessarily manufacturers. interchangeable between parfocalset of A objectives magnifications, have different but shoulder-to-intermediate the same height and shoulder the same image distance. As parfocal objec rotating turret, image change the focus. Biological objectives are aberra a objective. of glass between the object and the The design cover glass. metallurgical no objective assumes The optical tube length OTL of a microscope is point of the objective the front focalof po to point Standard values for the OTL are 160 mm and are mm Standard values for the OTL 160 image Newtonian distance: OTL is a The is assumed. Microscope Terminology Microscope Optical Length and NA Tube OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-32 14-31 Image Shown Object- Shown z Space Telecentric Intermediate Intermediate to the eyepiece image: presented ′ z  TUBE TUBE h f -f ece. The magnification ece. The magnification the of  TUBE f TUBE Tube Lens Tube  h, and an additional tube lens is used to  / / LOBJ  yf L OBJ objective, and a collimated beam results for collimated beam a and objective, TUBE Tube Lens Tube f OBJ f TUBE f  f u uy f    IOTL OBJ OBJ L OBJ y m m e usually designed using infinity corrected objectives. The The corrected objectives. infinity using designed e usually ented to the microscope microscope eyepi the ented to m e presented to the eyepiece. the to e presented Stop  F Objective OBJ OBJ OBJ f uu f - f Infinity Corrected Infinity OBJ - f Objective Object h Infinity Corrected Infinity objective-tube lens combination is: combination objective-tube lens each object point. There is no specific lengt is no each object There tube point. The intermediate image is pres Research-grade microscopes ar Research-grade microscopes the focal plane of object plane is the front intermediate produce the imag Magnification of Infinity Corrected Objectives Infinity Corrected Magnification of Infinity Corrected Objectives OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 14-34 14-33 YE E OBJ f 2 1 mm f 250 1 mf f     MP ( , Gaussian Diatances) ( , Gaussian quired to resolve two quired to the NA of the objective: ( , Gaussian Distances) ( , Gaussian 2 1   ( , Gaussian Distances) ( , Gaussian f f / / OBJ  f   hf OBJ OBJ EYE h TUBE TUBE fff solved Airy discs, and is termed Airy is termed discs, and empty solved ff  mm mm f  hzn hzn  R REYE z zf m        250 10 250         mzz  is just resolved with y to ease the visual observation. used be the eyepiece that is re VEYE  OBJ OBJ EYE  zf z itional information about the object. The extra The object. the itional information about mMP  visual magnification The visual magnification that is useful.  OBJ MP RK RR .61 /   W mm   hNA lescope or Binoculars (Afocal): Binoculars lescope or the Raleigh criterion is then: MP m MP z z 75 75 her magnify her magnify the just re    V OBJ EYE OBJ OBJ mm m m  mmMP z z hhmh .075 75 75  NA  OBJ 230 .55 .61 1.22 /#   EYE   V  V OBJ EYE hf hmh MP mNAm mmMP A maximum maximum visual magnification useful for the microscope results: A magnification. Some empty magnification ma magnification empty Some magnification. magnification magnification is applied to furt Magnification above this level yields no add level yields no this Magnification above From the discussion of magnifiers, the MP of magnifiers, of From the discussion the MP objects separated h'by min) arc is 1 the eye resolution of (using intermediate image separation at separation image intermediate Because of diffraction, there is a maximum maximum a there is diffraction, of Because Magnification of a Focal Imaging a Focal Imaging System: Magnification of Afocalan of Magnification System: Imaging a Magnifier: of Power Magnifying a Simple Te of Power Magnifying a Relayed Keplerian of Power Magnifying Telescope: Tube): (Finite Microscope a of Magnification Visual Tube): (Infinite Microscope a of Magnification Visual Rayleigh Criterion – object separation that the Magnification and Magnifying Power - Power Magnifying Magnification and Summary Microscope Resolution Microscope