Section 14. Relays and Microscopes

Transcription

1 Section 14 Relays and Microscopes 14-1 Image Erection The image produced by a Keplerian telescope is inverted and reverted. For many applications, such as terrestrial telescopes and binoculars, it is important that the image has the same orientation as the object. An image erection method must be added to the telescope system. Methods: Prisms Porro System Porro-Abbe System Pechan-Roo Abbe-Köenig Relay systems 14-2

2 Prism Speciication The erecting prism in a Keplerian telescope or binoculars is usually placed between the objective lens and the intermediate image. It must be sied so that the entrance and exit aces do not vignette the FOV. To minimie weight, the prism is usually as small as possible. The prism tunnel diagram allows the prism to be modeled as a plane parallel plate o glass. The prism geometry relates the sies o the prism aces to the length o the tunnel diagram. Consider the common Porro System: a a L = 4a 14-3 a Prism 1 Prism 2 Prism Speciication Telescope layout: FIELD The telescope layout is now modiied to include the tunnel diagram o the erecting prism system. The tunnel diagram (and thereore the prism) must be sied as to not vignette any rays or the speciied FOV or intermediate image sie. The prism dimensions are determined. XP 14-4 FIELD XP Reraction at the suraces o the plane parallel plate model o the prism must be included as well as the accompanying shit o the intermediate image plane.

3 Prism Speciication Reduced Tunnel Diagram The reduced tunnel diagram can be used to simply determine the prism sies without reracting the rays or shiting the intermediate image plane. An air-equivalent prism is used. The reduced tunnel diagram is sied so that all o the rays are unvignetted. a L = 4a a L/n = 4a/n FIELD 14-5 XP The physical sie o the prism can then be determined rom the sie o the reduced tunnel diagram on the schematic. TIR Limit in Prism Systems The astest /# or NA that a prism will support is limited by the loss o Total Internal Relection at the hypotenuse o the prism. Consider a right angle prism in air: n L ' ' º U º The top ray will lose TIR beore the bottom ray and thereore deines the NA limit. 1 C U 1 sin n 45 At the TIR limit: U C 14-6 sin nsin NA sin in air 1 n 1 45C 45sin NA sin nsin Limiting NA sin nsin 45sin n 1 1

4 14-7 TIR Limit in Prism Systems Limiting NA sin nsin 45sin 1 1 n Limiting NA nsin 45cos sin cos45 sin sin n n 2 2n 1 1 Limiting NA 1 2 n n Limiting NA n Limiting /# 2 Limiting NA Limiting /# n 1 1 Limiting /# index n TIR Limit Glass Choice Limiting /# BK7 n = BaK4 n = F2 n = I the objective lens is aster than the limiting /#, rays rom the edge o the pupil will not experience TIR. For ast objective lenses, higher index glass must be used. Limiting /# BK7 6 BaK4 4 F index n BK7 prisms are ound in older designs and lower cost systems. Note that the optical quality o all o these glasses (transmission, stria, etc.) are all excellent. Roo suraces do not experience this loss o TIR because the resulting compound angles increase the angle o incidence beyond the critical angle.

5 TIR Limit Eect on Exit Pupil The Porro Prism erecting system in a pair o binoculars can be thought o as our right angle prisms. I the objective lens used in the binoculars is aster than the TIR limit, portions o the XP are clipped. Porro Prism Systems Eye Lenses Nominal Exit Pupils 14-9 At each relection, the loss o TIR will clip an edge o the XP. Each o the our relections in a Porro Prism system will clip a dierent side o the XP. The inal XP becomes squared-o. In the regions o the pupil where TIR is lost, there will be some light in the pupil due to Fresnel relections. Relay or Erecting Lens A relay or erecting lens inserted between the objective and the eye lens o the Keplerian telescope can correct the image orientation. The intermediate image ormed by the objective is relayed to a second intermediate image. The second intermediate image is placed at the ront ocal point o the eyepiece. The re-imaging causes an image rotation o 180, correcting the image orientation. h 1 Relay Lens R R h 2 Eye Lens The net MP o the relayed Keplerian telescope is positive. The system MP equals the product o the magniication o the relay and the MP o the original Keplerian telescope. R mr R R MP mrmpk R

6 Relay Lenses and Field Lenses Field lenses can also be added at or near the intermediate images. A common arrangement is or each ield lens to image the pupil into the ollowing relay lens. All o the light collected by the objective is transerred down the optical system. The inal ield lens is part o the eyepiece. Eye Field Relay Field XP Lens ER The irst ield lens images the objective aperture into the relay aperture, transerring the entrance pupil to the relay lens. I the relay lens diameter is larger than this image, all o the light rom an object point collected by the objective will be transerred to the second image. For an optical system used with the eye, the inal ield lens will not image the relay lens aperture into the eye lens, but rather to the exit pupil with the appropriate eye relie. Ray Bundle with Relay Lenses and Field Lenses Eye Field Relay Field XP Lens The irst ield lens images the objective/stop into the relay lens. An intermediate pupil is located at the relay lens. ER Marginal Ray The relay lens images the irst intermediate image to the second intermediate image. This second intermediate image must be located at the ront ocal point o the eyepiece. The eyepiece is the combination o the second ield lens and the eye lens. The eyepiece also images the intermediate pupil into image space to create the exit pupil and the eye relie. In this example, the intermediate pupil is smaller than the relay lens diameter. A relay lens with a diameter smaller than that shown could be used. However in many situations, all o the lenses (except the objective) are mounted in the same tube and have approximately the same diameters.

7 Relay or Erecting Lens and Pupils Without a ield lens at the irst intermediate image, the relay lens produces the intermediate pupil. Relay Lens Intermediate Pupil In addition to creating an second intermediate image, the relay or erecting lens also produces an intermediate pupil. The eyepiece (ield lens and eye lens) projects the relayed image to ininity and transers the intermediate pupil to the XP o the telescope. The ER is o the telescope is changed. Relayed Relay Lens Image With a ield lens at the Field Lens irst intermediate image, the intermediate pupil is at the relay lens. Intermediate Pupil Relayed Image I the irst ield lens is not used, a larger diameter relay or erecting lens is required. O course, the relayed image must be located at the ront ocal point o the eyepiece. Glare Stop A physical aperture can be placed at the intermediate pupil to serve as a glare stop or stray or scattered light. Light entering the system rom outside the FOV can scatter in the system (such as rom the telescope barrel). The stray light is blocked by the glare stop. /Stop Relected/Stray Light Relay Lens Intermediate Image Relayed Image Intermediate Pupil and Glare Stop The glare stop should be the same sie as the intermediate pupil sie. Since the ocal length o the objective lens is typically much longer than the ocal length o the relay lens, the glare stop is then located just outside the rear ocal point o the relay lens The stray light will be superimposed on the irst intermediate image, but the stray light is blocked beore the relayed image is ormed. In certain applications (especially astronomy) the glare stop is also known as a Lyot Stop. In inrared systems, it is called a Cold Stop as it is cooled to reduce unwanted thermal radiation. I a ield lens is used at the irst intermediate image, the intermediate pupil is located at the relay lens, and the relay lens aperture can serve as the glare stop.

8 FOV and the Relay Lens In many systems, the relay works at approximately 1:1 conjugates or magniication. The object distance or the relay lens is then twice the ocal length o the relay lens. This situation limits the FOV o the system and/or requires a large diameter relay lens. The FOV is limited by vignetting at the relay lens. Relay Lens Relay 2Relay A ield stop and a glare stop can be added to this system. The glare stop would be located where the chie ray crosses the axis ollowing the relay lens. Since the FOV is small, adding a ield lens at the irst intermediate image plane may only provide a moderate increase in the FOV o the system. Erecting Couplet Increased FOV can be obtained by using an erecting couplet. The single relay lens is split into a pair o elements that provide the 1:1 imaging or the relayed image. Since the distance between the irst intermediate image and the irst element o the couplet is the ocal length o one o the relay elements, the cone o light rom the intermediate image has less distance to expand. A signiicantly larger intermediate image and FOV is supported. The FOV is still limited by vignetting at the relay lens Relay 2 Relay Relay Erecting or Relay Couplet The erecting couplet shown has the same diameter as the single relay lens o the previous slide.

9 Erecting Couplet - Pupils An intermediate pupil is ormed between the two relay elements, and a glare stop may be placed at this location. The second relay element will produce a virtual image o the intermediate pupil that is reimaged by the eyepiece to produce the exit pupil and eye relie. The common coniguration is or the two elements to be separated by twice the ocal length o a single element. Note that the system length has not changed as the separation between the two intermediate images remains 4 Relay. The magniication provided by the erecting couplet is independent o 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 o the inal intermediate pupil produced by the erecting couplet. Varying this separation allows the location o the exit pupil to be adjusted to produce the desired value or the eye relie Glare Stop Relay 2 Relay Relay Erecting or Relay Couplet Multiple Relays Multiple relay lenses can be used to transer the image over a long distance. Examples include periscopes, endoscopes and borescopes. Field Relay Field Relay Field A B C D E The image is transerred rom ield lens to ield 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 or transmission losses Starting with Lens B, a series o 1:1 imaging systems is oten used. All o the lenses will have the same ocal length and diameter. The relay system is completed with an eye lens or eyepiece. The inal image can also be placed on an detector array.

10 A Brie History o the Telescope September 25, 1608 Hans Lipperhay was provided a letter o introduction in order to present his invention to the States-General in The Hague o the Netherlands or the purpose o obtaining a patent: a certain device by means o which all things at a very great distance can be seen as i they were nearby, by looking through glasses 1608: Dutch (or Galilean) Telescope Lipperhay , German-Dutch t Erect image Usually a low magniication Oten short and compact Small ield o view Lipperhay s Patent Application September 25, 1608 October 2, 1608 Hans Lipperhay receives a request rom 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 ormed or the purpose o examining and trying the instrument in question on the tower o the quarters o His Excellency and to negotiate with the inventor about the abrication, within one year, o six such instruments made o rock crystal. December 15, Members o the committee report that they have seen the instrument or seeing ar with two eyes, invented by the spectacle-maker Lipperhay, and have ound the same to be good. However, since it is evident that several others have the knowledge o the invention or seeing ar, the requested patent be denied the petitioner, It is interesting to note that the development o binoculars began almost concurrently with the development o the telescope.

11 Galileo s Telescopes Galileo Galilei used a long high-magniication version o this design or his amous astronomical observations. Galileo produced his irst telescopes in 1609 (3-10X) with later improved telescopes with magniications up to 20-30X. In 1610, he published his observations on the moon, the moons o Jupiter and the constellations and the Milky Way (Starry Messenger). Other observations included the rings o Saturn, the phases o Venus and sunspots This 21X telescope rom has a plano-convex objective lens with diameter o 37 mm, an aperture o 15 mm, and a ocal length o 980 mm. The telescope is 927 mm long with a ield o view o 15 arc min. Galileo; , Italian Starry Messenger or Sidereal Messenger 14-22

12 A Brie History o the Telescope 1611: Astronomical (or Keplerian) Telescope Proposed by Johannes Kepler in 1611 Christoph Scheiner constructs irst Keplerian telescope in 1617 Inverted Image Higher magniication Longer length Good ield o view Kepler; , German t A Brie History o the Telescope Circa 1635: Christoph Scheiner introduces a single erecting lens to produce an erect image. Scheiner Erecting System or Two-Lens Eyepiece The ield o view is limited by the diameter o the erecting lens Scheiner; , German-Austrian Exit Pupil 2 Relay 2Relay Eye Erecting or Relay Lens Eye Lens

13 A Brie History o the Telescope 1645: Anton Maria Schyrle de Rheita ( ) used a two element erecting couplet to produce a practical terrestrial telescope with an erect image and acceptable magniication and ield o view. Schyrle Erecting System or Three-Lens Eyepiece Note the presence o a glare stop between the two erector lenses. Glare Stop Field Stop Exit Pupil Relay 2 Relay Relay Eye Erecting or Relay Couplet Eye Lens A Brie History o the Telescope 1662: Christian Huygens invents the two lens eyepiece incorporating both an eye lens and a ield lens. Schyrle-Huygens Erecting System or Four-Lens Eyepiece Huygens; , Dutch Glare Stop Field Stop Exit Pupil Field Relay 2 Relay Lens Eye Erecting or Relay Couplet Eye Piece Eye Lens In some telescopes, an additional ield lens was inserted at or near the irst intermediate image resulting in a ive-lens eyepiece.

14 A Brie History o the Telescope There is some evidence that the our-lens eyepiece was in use in the late 1600s, however it ell out o avor until the mid-1700s. While there were improvements to ollow, most notably the achromatic objective in the mid-1700s, the modern design orm o the terrestrial reracting telescope was irmly in place by this time. The use o brass tubes also began in the mid-1700s. The vast majority o telescopes produced were not intended or astronomical use, but or nautical and military purposes Microscopes The compound microscope is a sophisticated magniier which presents an enlarged image o nearby object to the eye. It consists o an objective plus an eyepiece or ocular. h O F O OTL Image o h Eyepiece MP h ER XP The visual magniication is the product o the lateral magniication o the objective and the MP o the eyepiece. m O O m m MP V O O MP 250mm 250mm Note that the visual magniication is negative ( O is negative).

15 Optical Tube Length and NA The optical tube length OTL o a microscope is deined as the distance rom the rear ocal point o the objective to the ront ocal point o the eyepiece (intermediate image). Standard values or the OTL are 160 mm and 215 mm. A relaxed eye (image at ininity) is assumed. The OTL is a Newtonian image distance: OTL F m m OTL 250mm mv The NA o a microscope objective is deined in object space by the hal-angle o the accepted input ray bundle. Along with the objective magniication, the NA is inscribed on the objective barrel. Microscope objectives are oten telecentric in object space. The stop is placed at the rear ocal point o the objective so that the magniication does not change with object deocus. E O O F NA n sin O O Stop Microscope Terminology The working distance WD is the distance rom the object to the irst element o the objective; can be less than 1 mm or highpower objectives. The mechanical tube length is separation between the shoulder o the threaded mount o the objective and the end o the tube into which the eyepiece is inserted. s and eyepieces must be used at their design conjugates and are not necessarily interchangeable between manuacturers. A set o parocal objectives have dierent magniications, but the same shoulder height and the same shoulder-to-intermediate image distance. As parocal objectives are interchanged with a rotating turret, the image changes magniication but remains in ocus. Shoulder Height 10X WD Biological objectives are aberration corrected assuming a cover glass between the object and the objective. The design o a metallurgical objective assumes no cover glass.

16 Ininity Corrected s Research-grade microscopes are usually designed using ininity corrected objectives. The object plane is the ront ocal plane o the objective, and a collimated beam results or each object point. There is no speciic tube length, and an additional tube lens is used to produce the intermediate image presented to the eyepiece. Ininity Corrected h F Stop Tube Lens - IOTL TUBE h Shown Object- Space Telecentric Intermediate image: presented to the eyepiece The intermediate image is presented to the microscope eyepiece. The magniication o the objective-tube lens combination is: m TUBE Magniication o Ininity Corrected s Ininity Corrected Tube Lens Object u u y L - TUBE -TUBE Intermediate Image m / u yl u y / L TUBE m TUBE

17 Microscope Resolution Rayleigh Criterion the object separation that is just resolved with the NA o the objective: h /# W NA Because o diraction, there is a maximum visual magniication that is useul. The intermediate image separation at the Raleigh criterion is then: h m h From the discussion o magniiers, the MP o the eyepiece that is required to resolve two objects separated by h' (using the eye resolution o 1 arc min) is MP.075mm 75m 75m h h m h A maximum useul visual magniication or the microscope results: 75m 75m mv m MP h.61 / NA m 230 NA.55m V Magniication above this level yields no additional inormation about the object. The extra magniication is applied to urther magniy the just resolved Airy discs, and is termed empty magniication. Some empty magniication may be used to ease the visual observation Magniication and Magniying Power - Summary Magniication o a Focal Imaging System: Magniication o an Aocal Imaging System: h / n m (, Gaussian Distances) h / n m h h 250mm 10 Magniying Power o a Magniier: MP Magniying Power o a Simple Telescope or Binoculars (Aocal): Magniying Power o a Relayed Keplerian Telescope: MP m 1 R MP m (, RMPK R R Gaussian Diatances) R Visual Magniication o a Microscope (Finite Tube): 250mm m (, V m MP Gaussian Distances) Visual Magniication o a Microscope (Ininite Tube): TUBE TUBE 250mm mv MP 2