502-13 Magnifiers and Telescopes

Home , Objective (optics), Relay 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 13-2 13-1 when viewed through the instrument? angular angular subtense of the image produced by ed when the object is placed at the optimum ed the object is placed at the optimum when e are characterized by a visual magnification magnification visual e are characterized a by quantity differ from instrument to instrument instrument instrument to quantity differ from Section 13 underlying principle remains principle remains the same: underlying angular subtense of the object. subtense of angular Magnifiers and Telescopes Magnifiers and How much bigger does an object How appear to be All optical systems that are used with the ey the with optical systems that are used All visual power. a magnifying or While this the details the definitions of of and for different applications, applications, different the for and viewing condition. the instrument compared to the to compared instrument the object the is measur The angular subtense of The size change is measured change in the size change is measured The as Visual Magnification OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-4 13-3 s convention 250 mm mm or 10 250 convention M u mm f   z  z z z  z f mm NP f     , the MP increases. A common assumption is common A increases. , the MP e object must e object placed inside the frontbe focalmust that provides an enlarged that provides an erect virtual image z hh  point of the eye, the eye, by point of e size of the image on the retina increases and e magnification eye possible with the unaided  h () () NP F 250 mm mm  250 250      P z hhfz  N  h  zs fzs () d () 250  NP   Angular sizeAngular of the image (with lens) f U M dfz U M u u Angular size of the object at the near point of the near at object size the Angular u  u  hf z   NP NP zf f z U M  dd ufzs u  MP d   h MP   m     MP MP d hz 111 zzf hz  h Unaided eye: With magnifier: With Note that as the eye-lens distance decreases that the lens is located at the eye 0): (s = The magnifying MP power magnifying The at (stop the eye): is defined as As an object is brought closer to the eye, eye, closer th to the an object is brought As the object appears larger. The largest imag point of the magnifier. occurs when the object is placed occurs when at the near from the eye. magnifier in A is a single lens of a nearby object for visual observation. Th Magnifiers Magnifiers –Power Magnifying OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-6 13-5 P N  the lens is close to the eye and that and the the lens is close to the eye  P N h d  ). 250 10" presented at the near point of the eye: presented at the near point of  ∞ U u  1 arc min1 arc rad .0003  NP mm mm dmm  mm 250 250 mm ff U 250 10" 250 10" 250 P N NP ff f h d d NP f  d NP NP  NP zf f z Ph MPh .003"/ dd .075 / 111 dmm M M  uMPu             Ph Pmmh Pzd     M M M MP MP MP   or Magnifiers Magnifiers to are up about 25X practical; is common. 10X The maximum MP occurs if the image occurs if the image is The maximum MP The magnification is a function of both f and the image location. The most common most common The the image location. and f both of function magnification The is a magnifier a that assumes of the MP definition of image is presented to a relaxed eye (z' = a presented to is image The angular subtense of the image image the at the eye: angular subtense of The Magnifiers –Magnifiers MP Required Magnifiers Magnifiers – – Power Magnifying Continued The human eye has a resolution of about 1 arc minute. A small object must be enlarged to enlarged be small object must A arc minute. 1 about resolution of a has eye human The determines This required the MP. arc seen. 1 minute to be 13-7 OPTI-502Optical Designand Instrumentation I

Telescopes are afocal or nearly afocal systems used to change the apparent angular size of an object. The image through the telescope subtends an angle ' different from the angle subtended by the object . The magnifying power MP of a telescope is

 MP  

MP 1 Telescope magnifies

MP 1 Telescope minifies

The angles  and ' are often considered to be paraxial angles.

u MP  Angular Magnification u

13-8 OPTI-502Optical Designand Instrumentation I

A Keplerian telescope or astronomical telescope consists of two positive lenses separated by the sum of the focal lengths. The system stop is usually at or near the objective lens.

fOBJ fEYE t = fOBJ f EYE

FOBJ u u FEYE u h z u

Objective Eye (Stop) Lens Image at Infinity This telescope can be considered to be a combination of an objective plus a magnifier. The objective creates an aerial image (a real image in the air) at the common focal point that is magnified by the eye lens and presented to the relaxed eye at infinity.

u fOBJ hufOBJ h uf EYE MP  ufEYE The image presented to the eye is inverted and reverted (rotated by 180° or “upside down”). The MP of a Keplerian telescope is negative. 13-9 OPTI-502Optical Designand Instrumentation I

A conundrum – to make the scene appear larger, the magnitude of the MP must be greater than one. This implies that the magnitude of the magnification is less than one. The image is smaller than the object. So how do telescopes work?

MP11 m 

Don’t forget about the longitudinal magnification. What is important is the angular subtense of the image compared to the object: the angular magnification.

mm 2 (in air)

hh mh mh u  h uu2 L LmLmLm h u u u 1 z MP 1 L um L

The image gets closer faster than it gets smaller, and the angular subtense increases. The scene appears foreshortened. Telescopes will list only the magnitude of the MP (10X, etc).

13-10 OPTI-502Optical Designand Instrumentation I

In an afocal system, rays parallel to the optical axis emerge from the system also parallel to the optical axis so the system has a power  = 0 or infinite focal length. This also follows from Gaussian reduction:

11 t 1212 ttff     12 ffff1212 ff ff  12 120 ff12 ff 12

The Gaussian imaging equations do not apply and the cardinal points are not defined.

For an afocal system, the lateral magnification is constant. Unless m = 1, there are no planes of unit magnification. Even if m = 1, then all planes are planes of unit magnification. In either case, the principal planes are not defined.

Similarly, the angular magnification of an afocal system is constant. The nodal points cannot be defined.

While it is acceptable to state that the focal points of an afocal system are at infinity, it is better to never talk about the focal points of an afocal system. Since rays parallel to the axis in one optical space never come to focus in the other optical space, there really are no focal points.

13-12 OPTI-502Optical Designand Instrumentation I

In most telescopes, the stop is at the objective lens to minimize the size and cost of this largest element. The objective lens also serves as the entrance pupil. The exit pupil is the image of the stop produced by the eye lens. The distance between the eye lens and the XP is called the eye relief (ER).

fOBJ fEYE t = fOBJ f EYE XP FOBJ u u FEYE z u h

ER Objective Eye (Stop) Lens Image at Infinity OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp YE E 13-14 13-13  YE E OBJ OBJ EYE 1     EYE OBJ  f f zf zf     zff ER z m f m  When the eye is in the XP, the eye the XP, When is in the ofentire the FOV telescope is seen. can rotate eye The look to within the FOV. around Ray bundles are shown for for are shown bundles Ray FOVs. different The eye will see only on-axis points. object near-axis) (or If displaced the eye is portions of the off- laterally, axis field are seen. YE E OBJ f OBJ EYE EYE f   1 OBJ   a simple way of determining the MP of the of determining a simple way MP of the    zff of the telescope to properly couple the two YE E EP EYE MP f Df  / OBJ OBJ PXP ff 1 E YE   E   mD D   OBJ EYE EYE OBJ EYE EYE OBJ EYE EYE fff  PD D   PEP EP    M X    D 111 ER z m f zf f f f f f 11 1 zf zzf XP XP   zER Exit pupil size: Exit pupil location: telescope system: A Keplerian telescope produces a real XP to the right of the eye lens. The XP of a visual of XP The the eye to the right of lens. Keplerian telescope produces a real XP A circle as the eye the Ramsden circle. instrument or is also known allows XP and Measuring diameters the the EP of The EP of the eye should be placed at the XP the eye should of The EP optical systems. vignetting can result: If the eye is not at the XP, Exit Pupil and The Eye Exit Pupil and Exit Pupil OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-16 13-15 the eye becomes the system system the eye becomes the level in the image. level the image. This is true even if in f. Microscopes may f. as little Microscopes may have as 2-3 a very long eye relief. For example, relief. eye example, a For long a very an the pupil of the eye so that vignetting does that vignetting the eye so of an the pupil mpensates for eye rotation as the rotation point the eye rotation as mpensates for allow the eye access Hand-held allow the eye to the XP. e XPs, while compact e compact XPs, while instruments may have s and binoculars is of the form the form s of is binoculars and The pupil translates translates The pupil with eye rotation. telescopes; one for each eye. P the eye, overfills the EP of P E M D  . XP mm in Diameter Objective D  AMP B (for example example 7X35) (for B X Binoculars are a pair parallel of telescope specification The on provided A not occur with head or eye motion. eye This co head or motion. occur with not the eye. at of eye is not the EP the of The XP should be made be made larger or smaller should The XP th A close match of the instrument XP and the eye requires EP precise alignment of the two Small pupils. displacements light will change the the eye is at the XP. under mm about 4 eye pupil diameter with a diameter mm, human varies 2-8 of The from conditions. lighting ordinary the instrument of the XP When stop. Larger instruments tend to have larg mm). (1-1.5 diameters XP small to Sufficient eye be provided relief should instruments should have 15-20 mm of eye relie riflescope needs a large to avoid ER problems due to kickback. mm eye relief. have systems should Other mm of Telescope and Binocular Specification Binocular and Telescope Exit Pupil and Eye Relief Exit Pupil and 13-17 OPTI-502Optical Designand Instrumentation I

A 5X Keplerian telescope is constructed out of two thin lenses. The separation between the two lenses is 120 mm, and the diameter of the objective lens is 25 mm. The system stop is at the objective. Determine the eye relief and the diameter of the exit pupil for this telescope. [ ] a. ER = 20 mm and DXP = 10 mm [ ] b. ER = 24 mm and DXP = 10 mm [ ] c. ER = 20 mm and DXP = 5 mm [ ] d. ER = 24 mm and DXP = 5 mm

13-18 OPTI-502Optical Designand Instrumentation I

fOBJ f t = fOBJ f EYE = 120mm EYE XP FOBJ

FEYE h z

ER Objective Eye (Stop) Lens DSTOP = 25 mm 13-19 OPTI-502Optical Designand Instrumentation I

Telescope Design 5X Keplerian:

fOBJ MPfftfffmm55 OBJ  EYE  OBJ  EYE  6120 EYE  fEYE

fmmfEYE20 OBJ 100 mm

Eye Relief – Image Stop Through the Eye Lens:

11 1  zff  OBJ  EYE   t 120 mm zzf EYE

zERmm 24

Exit Pupil Diameter: DEP Dmm STOP  25

zmm 24 mXP  0.2 zmm120 D 25mm or D EP 5mm XP MP 5

DXPm XP D STOP 0.2 25 mm  5 mm

13-20 OPTI-502Optical Designand Instrumentation I

The resolution of the eye is about 1 arc min:

 1 arc min

 1 arc min   MPMP

The visual resolution has been minified into object space.

If two objects are separated by , the minimum MP to visually resolve them is:

1 arc min MP  MIN 

For critical work, MPs larger than this value are often used to minimize visual fatigue. There is often no need to work at the visual resolution limit. OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-22 13-21 W 2    rf //# 2.8 1.5 7.1  rf Pedrotti & Pedrotti & Pedrotti 83.9   1 J is the radial is the radial coordinate, 2//#    r 0 is a Bessel function, and f/# is a Bessel function, and  0 0 1 0 where J is the image is the image space f-number. EE on free system, on Airy Disk free system, an 0 r 3 r f/#f/#f/#f/# E 0.0041 f/# 0.0 E 0.0016 0.0 0.0 f/#f/# 0.0 E 0.017 2        r Radius rRadius E Peak in Ring Energy % 1 r image aberrati For an image spot. 0 E E The pattern has a bright central core surrounded by rings. by central a bright pattern The core has surrounded Third ZeroThird ZeroFourth 3.24 4.24 Second Zero 2.24 First Zero 1.22 Central Maximum 0E 1.0 Second Ring RingThird 2.66 3.70 First Ring 1.64 Because light is a wave, it does not focus to a perfect point image. to a perfectfocus image. Diffraction not point it does Because light is a wave, from the the of size the aperture limits produced: is pattern Airy Disk Diffraction OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-24 13-23 R P E f D  P /# E f f D P E D P E  D  f 1.22 /   1.22 / termining a termining the best possible resolution for  1.22 / # 1.22  m, and   f   in microns   f/#    1.22 / # Rf f  f/# ≈ D D = 2.44 one image falls on the first zero of the other image. separation image. The the other image the first of zero one falls on is approximately 0.5 is approximately Resolution Angular Resolution  In visible light, In The Rayleigh resolution criterion objects can be states two point that the images of of resolved if the peak disk: the Airy of equals the radius image the focal length (or distance): by dividing by resolution is found angular The The diameter The diameter Airy the is of Disk de for useful approximation very is a This given f-number. Rayleigh Resolution Airy Disk Diameter Airy Disk 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 13-26 13-25 XP  Unvignetted Fully Vignetted (the limit Vignetted Fully passes one ray when XP) through the  EYE f  P  E z z D minimize minimize It is easier visual effort. view to rd1 mrad MP EP μ  D solution, the maximum useful MP is obtained: useful MP solution, the maximum 138 d the FOV As vignetting at the eye lens. by 1000  points or the angular separation two separation the angular or of points is extra MP is termed is termed Empty Magnification. is extra MP  this angle is magnified the MP: this angle is magnified by m is in mm: is in  μ arc sec XP XP  EP perspective of the objective lens. lens. objective the perspective of MP EP  D 138 EP EP 1.22 0.55  m, m, and the D EP EP EP  0.43 mm in DD D MP  1.22 1mm 180 3600arc sec 138arc sec 1 arc min1 60 arc sec arc sec       50% Vignetted Angular ResolutionAngular 1.22 /  EYE EYE  MP D D f = 0.55  f     when not at the visual resolution limit. at the visual resolution Th not limit. when Beyond this MP, no image improvement results as the Airy are discs Airy magnified. just being image results as the improvement no this MP, Beyond to Magnifications limit several times this are used In the telescope image space or eye space, space or telescope image the In intermediate image points from the from points image intermediate The angular resolution based on the Rayleigh criterion criterion the Rayleigh on is resolution based angular The object two separation of is the angular This that Assuming Diffraction-Based Resolution Diffraction-Based Telescopes –View of Field When this Rayleigh resolution eye equals the re or intermediate the eye intermediate lens. or is clipped by image height increases, bundle the ray The FOV of the Keplerian of telescope The FOV is limite OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-28 13-27 z z XP Rays Vignetted Previously Here the field stop limits Here limits the field stop the to the 50% vignetted FOV. FOV XP Eye Lens Eye EYE intermediate image plane to restrict or restrict to plane image intermediate - f creased a fieldaddition of lens. This by the e, and it bends the chief ray its of the chief ray and bundle it bends e, and onsideration. In a simple telescope, Keplerian simple a In onsideration. e angular size of the field stop as seen by the seen by the field stop as angular size e of to limit limit to a well-corrected the field to non- or FIELD f to the aperture of the eye lens. Field Lens EYE f  Field Stop Objective Rays from Rays objective lens. definesThe field the maximum stop chief ray angle forthe system. chief ray A the field stop. by a larger is blocked to FOV corresponding lens is placed at the intermediate image plan the angular field of view of a telescope a view of is th field of the angular in the instrument can be of view field of The rays in back towards the axis and vignetted region. This is often a cosmetic a cosmetic often is c This vignetted region. A field stop is a physical field stop is aperture A placed at an limit the system This FOV. aperture serves Field Lenses Field Stop 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 13-30 13-29  XP  YE YE P P E E OBJ E IELD 2 f f F M D f f ER   P    XP  Eye ER ER d Lens D d MP  d  z EYE f P z XP 1/ Field Lens XP ER has the same has the same size lens. the field as without  Assume thin lenses with a separation The MP of the telescope of is unchanged. The MP EYE f ER relief. Maintaining a usable ER limits relief. Maintaining limits a usable ER the ER e possible for a given eye lens diameter. lens diameter. e given eye a possible for 2 P mains at the eye lens. As a result As the mains at the eye lens. e lens is called an eyepiece. Gaussian ane, dirt and imperfections on it become part it become imperfections on and dirt ane, e telescope or the size of the XP. The XP e telescope the XP. or the size of  ttf is often displaced from displaced is often from the image plane to d Eye Lens Eye Eye Lens Eye  EYE P EYE EYE YE EYE - f E - f IELD FIELD F ff ff EYE ff f f  IELD EYE EYE YE FIELDYE EYE FIELD EYE EYE EYE  EYE EYE F E E FIELD   f             dt ff   dtf Field Lens The field lens shifts the rear principal plane d'. original eye relief by reduce the to magnification of the stop is unchanged. The XP magnification XP The of the stop is unchanged. The front principal the eyepiece The front plane of re The eyepiece power equals the eye lens power. The eyepiece eye equals the lens power. power Since the field lens is located at an image Since the field lens is located at an image pl the image. of In practice, the field lens strength of the field lens and the FOV increas the FOV the field lens and strength of defocus. through effects these minimize moves closer moves to the eye eye reducing the lens The field lens does not change the MP of th of MP change the not field lens does The The combination The combination of the field lens and the ey reduction the eyepiece. easily gives the power of the focalthe eye lens: length ofequal to Field Lenses –Field Lenses Summary Field Lens –Field Lens Combination Lens Eye OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-32 13-31 te image plane serves plane te image z between the two elements. between the two elements. z fiducial are they and marks, XP XP design variations exist. In both of these more eye relief than the Huygens eyepiece. eyepiece. Huygens the more relief than eye EYE s not change the magnification s not change the magnification or size of the EYE eyepiece are the Huygens the Ramsden and f f eld stop at the intermediate at the intermediate eld stop image plane. om the intermediate image plane. The two The plane. image intermediate the om the field lens and the eye lens. A simple the eye A simple the field lens and lens. cated at an intermedia an cated at intermediate intermediate image plane to restrict the mm to other optical instruments such as YEPIECE E f 250 Field Stop  FIELD f e plane to be superimposed on the image. the e Since both the image. superimposed on plane to be forHuygens eyepiece a falls FIELD alignment alignment measurement and f EYEPIECE MP Field Stop A Kellner A eyepiece replaces the Ramsdenthe singlet lens of eye eyepiece with a doublet for color correction. The Ramsden intermediate the eyepiece places field the lens behind image. It is a good with reticles choice to use as the eyepiece doe intermediate image. This eyepiece has about 50% about has eyepiece This image. intermediate It is good practice It displace is good to lens fr the field eyepieces compound general classifications of historical and specific of number great eyepiece. A configurations, it is also common configurations,place to a fiit is also common The intermediate image plane An eyepiece or ocular is the combination eyepiece An or ocular is the combination of eyepiece does not have a field lens. eyepiece A compound has an eye both lens and a field lens. The properties eyepieces of are applicable microscopes. The eyepiece contain field stop at the can a system aperture system The a fieldFOV. of lens lo a field stop. of the function graticlesReticles and provide placed in the intermediate placed in the intermediate imag reticle and the image reticle the image are focus,and in reticles defect be clean and must free. an eyepiece a magnifier: The MP ofthe same as that is defined of Compound Eyepieces Compound Eyepieces OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-33 13-34 z Eye EYE OBJ  f f  z  f   EYE   .  ′ OBJ  EYE YE OBJ F F  E MP f 10 EYE  EYE f f    Eye Lens Eye  OBJ f ER z m f and emerge and emerge at   EYE f Eye Lens Eye OBJ EYE ope at a larger angle. The image appears V of the system There the system ofis no is small. V nd a negative lens to obtain an erect image an erect a negative lens to obtain image nd ssible to the eye. There is poor coupling poor is There eye. the ssible to t = ft = f 1 xpensive systems as opera glasses. xpensive systems such OBJ f OBJ EYE 01    tf f Objective EYE OBJ f f EYE OBJ  f f OBJ f   Objective    mm MP MP bigger to the eye. the bigger to For a Galilean For a telescope constructed, to be the negative stronger positive lens must be than the lens. The XP is internal or virtual acce not and The XP between the telescope the eye, FO and and intermediate intermediate with reticles. used it cannot be image so plane, The Galilean telescope for ine is used Image at Infinity and a positive MP (MP 1). and > The Galilean telescope uses a positive lens a Galilean Telescope Galilean Telescope Collimated Collimated input light comes out of the telesc The image in this configuration is erect (right-side up). Rays from off-axisRays from object an enter telescope the at 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 13-36 13-35 z EYE f EYE f z Eye Lens Eye  EYE   f OBJ EYE fied erect This 1). image (0 < MP < P ide-down and must ide-down and must be corrected with image  OBJ EYE 1 M tf f    tf f Erect Image m 01 ope is shorter than the corresponding Keplerian Keplerian ope than the corresponding is shorter EYE OBJ f f Objective peepholes and many camera camera many these systems, In peepholes and viewfinders. OBJ f OBJ EYE  EYE  OBJ tf f F F P M OBJ OBJ f f The image Keplerian The image in the telescope is ups erecting prisms or a relay erect order obtain an lens in to image. Equivalent KeplerianTelescope: Galilean Telescope: For For a given , the Galilean telesc telescope. Its FOV is also smaller. telescope. Its FOV configuration is used in door in door is used configuration A reversed Galilean telescope provides a mini a Galilean telescope provides reversed A the eye the system is often stop. Reversed Galilean Telescope Comparison of Galilean and Keplerian Telescopes Keplerian and Galilean of Comparison OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-38 13-37 Myopia Shown for Shown Parabola Parabola Parabola rmediate image at the at image rmediate EYE f EYE  z e image e image presented the eye to ected to infinity for viewing viewing infinity for ected to   d eye is no longer at infinity. The far is far point The at infinity. longer d is no eye actice they often deviate from this condition. condition. this deviate from actice often they OBJ EYE justed to place justed to the inte  Hyperbola OBJ EYE   tz f tf z Ellipse hout accommodation. The distance from The distance from the hout accommodation. OBJ  iece adjusted to place th can be OBJ ity, the image must still be proj be still must image the ity, z f Far Point The choice of specificthese the aberrations The choice of for telescopes conics used is based on and imaging properties the conic surfaces. of Cassegrain telescope: The The telescope: Cassegrain the positive primary combination of is the with a negative secondary telephoto a of equivalent mirror objective. Newtonian telescope: A positive A Newtonian telescope: mirror flat. It is directly with a fold analogous to a Keplerian telescope. Gregorian telescope: The The telescope: Gregorian is mirror primary positive positive a second by followed intermediate the relay to mirror with the analogous As image. an telescope, Keplerian relayed produced. is erect image Of course, both corrections corrections Of course, both can be combined. With refractive error, the far point of the relaxe the of point far the refractive error, With the object distance wit that in focus is eyep the to image intermediate at its point. far While While telescopes are defined to be afocal, pr in When the object is not at When the object is not infin with a relaxed eye. The telescope length is ad front focal point of the eyepiece front focalof point (or magnifier). Mirror Based Telescopes Mirror Based Focusing a Telescope OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-40 13-39 z = 10 = 15 EYE f OBJ EYE used with the eye. = 20 a = 30 a OBJ EYE  to an afocal system afocal system to an  OBJ EYE tion is determined tion is determined the pixel size the or by em em used to view distant objects. In this .06 15 EYE OBJ  ymy tf f nd fully-vignetted nd fully-vignetted FOVs of this system? real image the telescope real by falls image on produced 300 0 15 ( .06)(300) 3 15 quates an angular size object to in space. = 250 D = 50 D 250 since stop is at the objective. the    OBJ EYE OBJ f other parts of the instrument. the parts of other  u  OBJ OBJ OBJ   u     EYE OBJ      yyutu uu y EYE OBJ  yyut uy y t = 300t = f OBJ f u Chief Ray: The chief ray height at the eye lens depends on the FOV. the FOV. on lens depends height at the eye chief ray The FOV. of is independent ray marginal The Vignetting will occur at the eye lens, Marginal Ray: What What are half-vignetted the unvignetted, a Keplerian Telescope:Keplerian 5X-1/5 = m Vignetting Example Telescopes and Imaging Detectors Imaging and Telescopes The image relayed The image can also be to aberrations, and resolu the diffraction Ignoring the detector array. The detector placed at image is plane. an Refracting: Reflecting: The pixel size e film. resolution the of The term The term telescope mean to any syst has come refers specifically telescope a discussion, formal astronomical telescopes Large are actually objectives cameras or image an array where detector placed is at the system focal point. examples of imaging these detectors are arrays CDD With film. and photographic Two detectors, an eye lens is not used and the OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-42 13-41 1  10 tan  250   10 YE E  Uu a IELD F t FIELD a  It’s an image image plane! an It’s and and diameter diameter 20 is added to the 5X Keplerian 250 not required not required to do this calculation. This .02333  .03333 .04333 u base Keplerian telescope results. base u u 7 10 1.34° 300 1.91°  13 300  u 2.48°  300     15 ( .06)(250) 0             YE EYE EYE EYE EYE EYE EYE EYE EYE EYE EYE EYE 2.29° E u U ayy u U 10 300 3 ay ay u .04 U 10 300 10 3 ayy ay 10 300 3 10 3   IELD FIELD FIELD  F FIELD OBJFIELD FIELD FIELD FIELD U ayy u 10 250 yyut y yutu = 0, all of the vignetting conditions collapse to one. all the vignetting conditions collapse to one. of 0, = FIELD FIELD An almost 2X improvement An almost 2X improvement over the the field lens was Note that the power of position the exit prevent to vignetting at the eye lens and/or to be used can power pupil (eye relief). Since y The field lens is in an image it an image plane, and serves as a fieldThe field stop. lens is in Unvignetted Field: Half Vignetted: Fully Vignetted: At the eye lens – Unvignetted: What What happens to the FOV if a field lens of telescope? At the field lens: Vignetting Example Vignetting Example –a Field Lens Add Vignetting Example Vignetting Example – Continued OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 13-44 13-43 2.29° 1.91° 2.48°    1.34° U U  U U 100  25   FIELD f d Half Vignetted: The ER is reduced from to 35. 60 from is reduced ER The With Field Lens: Field With Fully Vignetted: Vignetting Example Vignetting Example –Keplerian 5X Vignetting Example Vignetting Example –Keplerian 5X Unvignetted: 13-45 OPTI-502Optical Designand Instrumentation I

In most Galilean telescopes and binoculars, the eye serves as the system stop. The system FOV is limited by vignetting at the objective lens. Note that these systems are not always well defined as there is no prescribed location for the eye relative to the eye lens (no external XP).

Consider this example of a 3X system:

fOBJ = 150 mm FOV = 0° fEYE = -50 mm

t = 100 mm

ER = 25 mm Eye fOBJ tf  f f ER OBJ EYE EYE Pupil Pupil Dia = 4 mm FOV = ±1°

DOBJ = 30 mm

DEYE = 10 mm The half vignetted object space FOV is about ±1.6° MP = 3 Vignetting occurs at the objective lens.

13-46 OPTI-502Optical Designand Instrumentation I

When looking through a Galilean telescope, it appears that you are looking through a hole well out in front of the telescope. The hole is the image of the objective lens through the negative eye lens. Vignetting at the objective lens usually limits the FOV of a Galilean telescope.

The apparent size of the image of the objective lens (the hole) as viewed from the eye determines the half-vignetted FOV and the chief ray at the eye.

D f ER Eye OBJ EYE Pupil -

DOBJ Stop zOBJ

u

u zOBJ

11111  zzf  tf Using the 3X telescope design: OBJ OBJ EYE EYE *Obvious result: the objective is in object space zmm 33.33 fEYE = -50 mm OBJ of the telescope and the objective image is in image z  t = OBJ = 100 mm mzOBJ /0.3333 z OBJ space. The diameters must be related by the telescope DOBJ = 30 mm  DmmOBJ 10 magnification. 13-47 OPTI-502Optical Designand Instrumentation I

The apparent size of the image of the objective lens (the hole) as viewed from the eye determines the half-vignetted FOV and the chief ray at the eye. The chief ray in object space also goes through the edge of the objective lens.

D f ER Eye OBJ EYE Pupil -

DOBJ Stop

u u

zOBJ

D /2 5 mm utan OBJ  ERz OBJ 58.33 mm zmmOBJ 33.33  Dmm 10  4.9 MP  OBJ  ER 25 mm   1.6 MP

This is the half-vignetted FOV of the telescope. Note that the FOV depends on the value of the Eye Relief or where the telescope is placed relative to the eye.

13-48 OPTI-502Optical Designand Instrumentation I

An autocollimator is a widely-used metrology tool for alignment and angle measurement. It is the combination of a collimator and a viewing telescope. The same objective lens is used for both. A point source is placed at the focal point of the objective, and the resulting collimated beam is reflected back into the telescope by the target mirror. The displacement of the returned beam on a measurement reticle measures the mirror tilt.

Point Objective f O Source 

2

Reflecting BS Reticle Surface

Image displacement in the reticle plane:

D  2 fO

This displacement is independent of the distance to the test surface. OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp 13-49 Ch 4, D. Goodman Ch 4, D. (D. Goodman Malacara, Ed.) ngles and to align parallel to align parallel ngles and surfaces. Other ed for commercial ed for commercial autocollimators. Geometrical and Instrumental Optics, Instrumental and Geometrical Resolutions of 0.1 arc 0.1 sec are quot Resolutions of References: Metrology with Autocollimators, Autocollimators, References: Metrology Hume with Roof test (two returned spots): angles (with a pentaprism): Right Surface flatness: applications include: The autocollimator The autocollimator to measure is used tilt a Autocollimator Applications Autocollimator