Review and Practical Application of Telescope Optics

Transcription

1 Review and Practical Application of Telescope Optics William L. Brown, OD, PhD, FAAO Mayo Clinic Rochester, MN Please silence all mobile devices and remove items from chairs so others can sit. Unauthorized recording of this session is prohibited.

2 Learning Objectives Following the lecture the participant will be able to: Compare and contrast Keplerian and Galilean telescopes (TS) Describe factors that affect image brightness through a telescope. Describe factors that affect field of view through a TS Give reasons that a Galilean TS might be easier to use than a Keplerian for seniors. Describe why an afocal TS must be modified to view a near object and methods by which modification is done

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4 Magnification Field of view Image brightness What are important features of TS? Alignment with eye to optimize field of view & brightness

5 Telescopes (TS) used in Low Vision Create enlarged retinal image through angular magnification Used, rarely, in reverse to create minified image for field awareness (will not be discussed in this lecture) Distant object (subtending angle at eye) Distant object (subtending angle at eye) Image from TS subtends enlarged angle at eye) Retinal image Retinal image (enlarged & inverted)

6 Objective (OBJ) Power = Gathers light If object at, it forms image at its focal plane, Eyepiece (ocular) (EYP) Power = Magnifies the angle subtended by the image to be viewed by eye Let s look inside a simple 2-lens telescope (TS) Objective (OBJ) f o ' f e Eyepiece (EYP) For emmetropia or properly corrected ametropia, focal plane of eyepiece is at image from objective

7 Afocal setting Focal points, and, coincident Image of distant object formed by objective is at Object for eyepiece is at, so final image is at Parallel in (distant object, zero vergence) Parallel out (image at, zero vergence) Objective (OBJ) f o ' f e Eyepiece (EYP) Note: These concepts apply to both Keplerian and Galilean TS, as described later

8 Angular magnification Image magnification f o ' f e For enlarged image eyepiece is stronger power: > For smaller image objective is stronger power: > OBJ EYP Upright or inverted?? M (+) Upright image M (-) Inverted image

9 Bailey et al., Berkeley Yellow Pages

10 Bailey et al., Berkeley Yellow Pages

11 2 types of refracting TS Keplerian Galilean (+) (+) OBJ EYP + Eye projects image below axis Keplerian (+) (-) ' OBJ + Galilean EYP - Eye projects image above axis

12 Keplerian TS Objective (+) Eyepiece (+) Inverted image Prism used to form upright image for low vision use BUT the equation doesn t know about the prism Object OBJ OP = f o + f e Fo Projected Image EYP Afocal setting: Optical path separation (OPS) betw. OBJ & EYP = sum of focal lengths (absolute values) Note: OPS physical separation between OBJ & EYP when OP is folded by a prism Note the effect on field

13 Example (Keplerian) Assume +20D objective +100D eyepiece Find magnification and separation between objective and eyepiece. = +20 D f o ' = +50 mm OBJ EYP Sep.= f o + f e = +60 mm f e = -10 mm = +100 D F o f o = 1000/ = 1000/(+20) = +50 mm f e = -1000/ = -1000/100 = -10 mm Image 5x larger, inverted. Separation = f o + f e = (10) = 60 mm

14 Objective (+) Eyepiece (-) Upright image without prism Galilean telescope (+) (-) OBJ + Galilean EYP - ' Eye projects image above axis Afocal setting length = difference between focal lengths (absolute values)

15 Example (Galilean) Assume +20D objective -50D eyepiece Find magnification and separation between objective and eyepiece. Image 2.5x larger, upright (relative to object). OBJ f o f e = +30mm f o ' = +50 mm ' Image of OBJ f e = +20 mm EYP f o = 1000/ = 1000/(+20) = +50 mm f e = -1000/ = -1000/-50 = +20 mm Separation = f o - f e = (20) = 30 mm

16 Prism to give erect image in Keplerian TS: 1) Double porro prism Double Porro prism (has elbow) Binocular with double Porro Binoculars#/media/File:Binocularp.svg Beecher binocular /commons/e/ed/double-porro-prism.png

17 Pechan Schmidt prism (Co-axial) 2) Pechan Schmidt prism Monocular with Pechan Schmidt /commons/9/93/schmidt-pechan-prism.png LVhtml/CatalogPDFs/SpiralEFTel.pdf Designs for Vision Binocular 6.0X Expanded Field Telescopes,

18 3) Roof pentaprism Roof Pentaprism Ocutech VES-SPORT-II Patented telescope/periscope combination OCUTECH By DrBob at the English Wikipedia, CC BY-SA 3.0, OCUTECH, Inc.

19 Controlling image brightness Entrance pupil Limits brightness for axial object by limiting the diameter of the axial pencil that makes it thru the TS. Ent. Pupil does NOT limit the field of view that s the job of the field stop For Keplerian, objective is ent. pupil Exit pupil Image of entrance pupil thru eyepiece Distant object point on axis D J Objective Entrance pupil l F o Eyepiece Exit pupil J D Eye relief l' = l/m Eye relief Distance from eyepiece to exit pupil Glasses can push observer s entrance pupil away from exit pupil

20 For TS alone Entrance pupil is OBJ Exit pupil (image of ent. pupil thru eyepiece) is internal For TS w/ eye: Entrance pupil of eye (not the OBJ image) is the exit pupil for the system Entrance & exit pupils Galilean TS OBJ f o f e f o ' ' Image of OBJ f e EYP Objective of the TS limits the field of view through the TS/eye system

21 Bring in the observer Time out to review eye s entrance pupil & aperture stop Aperture stop Element in the system (i.e., eye) that physically limits the diameter of an axial pencil that reaches the image In the eye, it s the pupil, so actual physical limitation is inside the eye Entrance pupil of observer Entrance pupil diameter of obs. = E O Image of the pupil through the cornea Limits the diameter of the object space pencil entering the eye that will make it to the image Ent. pupil Q E O Q Pupil = Aperture stop

22 Representing the eye s entrance pupil henceforth For simplicity, let the solid borders of the opening in the eye represent the entrance pupil, the most important opening for consideration with TS. This opening interacts directly with pencils of object rays entering the eye Ent. pupil E O Pupil

23 Effect of observer s entrance pupil diameter on retinal image illumination Let: I = illumination of retinal image D = entrance pupil diameter A = entrance pupil area Example: Compare ret. Illum w/ 4 mm pupil vs 3 mm pupil: I 2 /I 1 = 3 2 /4 2 = 9/16 = 0.56 I 2 56% I 1 Larger ent. pupil Smaller ent. pupil D 2 Area A 1 A 2 D 1 Forget the TS for a minute. Think of the impact of changing the pupil size from 4 mm to 3 mm I 1 w/ 4 mm pupil Same image area I 2 w/ 3 mm pupil

24 Ideal situation for maximum image brightness: Coincidence of observer s ent. pupil & TS exit pupil Pencils from 2 separate distant points All light passing through TS entrance pupil passes through TS exit pupil Observer s entrance pupil ideally at exit pupil of TS Not always possible, never with Galilean TS Interacts with observer s entrance pupil to affect brightness D J Objective Entrance pupil f o ' F o f e Eyepiece J Observer D Exit Pupil of TS at eye s ent pupil

25 TS Entrance/exit pupil diameters & angular mag AND ALSO Distant object on axis D E TS J OBJ Entrance pupil l F o EYP Exit pupil J D Eye relief l' = l/m E TS

26 Entrance/exit pupils to calculate M D J J D = = 25 = = 3.6

27 Effect of TS angular mag. on image area A = Retinal image area without TS Without TS y A A =Retinal image area with TS A = (M) 2 A Distant object With TS w/ M M A y A = y 2 A = M 2 A M A y Example: How much larger is the area of the image than the object for a 2x TS? A TS = 2 2 x A w/o TS = 4 A w/o TS A = (My) 2 = M 2 y 2 = M 2 A

28 Effect of patient s entrance pupil diameter - Depends on its size relative to exit pupil of TS 1) Let pt. s entrance pupil diam. = TS exit pupil diam. Ent. pupil of eye at Exit pupil TS In this case, A EnTS = M 2 A EnPE (since TS exit pupil A = AEnPE Effective entrance pupil for the TS is image of ent. pupil of eye through eye piece Area of this image is M 2 larger than ent. pupil of eye, so M 2 more light collected than for eye w/out TS. E TS M 2 A EnPE = A EnPTS Ent. pupil TS Image of Ent. pupil eye thru EYP F o EYP Ent. pupil eye E E A EnPE E TS =E E Exit pupil TS E TS

29 Pt. entrance pupil diam. = TS exit pupil diam. BUT!! Area of retinal image with TS is also M 2 larger than w/out TS. M 2 more light for M 2 more retinal area means retinal image illumination is same w/ TS as w/o TS.

30 Effect of patient s entrance pupil diameter - Depends on its size relative to exit pupil of TS 2) Consider if pt. s entrance pupil diam. < TS exit pupil diam. Image of ent. pupil of eye through eye piece limits entering rays Area of this image is M 2 larger than ent. pupil of eye, so M 2 more light collected than for eye w/o TS. BUT!! Area of retinal image with TS is also M 2 larger than w/o TS. M 2 more light for M 2 more retinal area means retinal image illumination is same w/ts as w/ots. E TS M 2 A EnPE Ent. pupil TS Image of Ent. pupil eye thru EYP F o EYP E TS E E Ent. pupil eye Ent. pupil of eye at Exit pupil TS A EnPE Exit pupil TS

31 Effect of patient s entrance pupil diameter - Depends on its size relative to exit pupil of TS 3) Consider if pt. s entrance pupil diam. TS exit pupil diam. In this case, TS exit pupil (& therefore also the objective) limits the light reaching the retina Area of image of ent. pupil of eye through eye piece is M 2 larger than ent. pupil of eye and is larger than ent pupil of TS is M 2 larger than exit pupil of TS Compared to Cases 1) & 2), amt. of light entering eye (and retinal illum.) is reduced by (A ExPTS /A EnPE ). E TS M 2 A ExPTS Ent. pupil TS Image of Ent. pupil eye thru EYP F o EYP Ent. pupil eye E TS E E Ent. pupil of eye at Exit pupil TS A ExPTS Exit pupil TS

32 Example of Case 3) Assume entrance pupil of eye is 4 mm and a 4X12 Keplerian TS is used. How much is the retinal illumination changed by using the TS? Solution: TS: Exit pupil diam. = 12/(-4) = -3 mm A ExPTS /A EnPE = (-3) 2 /(4) 2 = 9/16 = 0.56 Ret. Illum. w/ts = 56% of the ret. illum. w/o TS

33 TSs reduce the amount and quality of retinal illumination for other reasons Reflections from surfaces of multiple elements (lenses, prisms) Keplerian affected more than Galilean b/c of more elements Anti-reflection coatings help Image quality affected by: Stray light inside the TS from peripheral light reflecting off housing of TS Quality of lenses Precision of alignment of the optical components All of these impact cost & weight

34 Labels on telescopes 7 X o 7 = M = Angular magnification 25 = Objective diameter (mm) 10 o = True field of view (object space) Object space Angular extent of the object visible through the telescope Eyepiece Objective

35 Field stop Aperture in the TS that limits the field of view (FOV) Not the entrance pupil Often the diameter of either: The field lens in multielement eyepiece OR A close-by aperture OBJ f o ' = xm A = true (object) FOV = apparent (image) FOV F o Field stop f e EYP

36 What is a field lens? No Field lens Field stop Lens placed at or near secondary focal plane of OBJ Increases field of view Reduces diameter needed for eye lens Generally part of the eye piece Intercepts rays from peripheral objects that would otherwise miss the eye lens and redirects them into the eye lens Only in Keplerian TS Rays from distant object Rays from distant object OBJ OBJ Field lens F o Field stop F o No field lens Field lens Eye lens Eye lens

37 Keplerian telescope Remember we said earlier: Coincidence of ent. pupil of eye w/ exit pupil of TS is ideal For optimum brightness & field of view Fo Exit Pupil TS Ent. Pupil Eye Object OBJ Ent.pupil EYP

38 Keplerian telescope: What if Ent. pupil of eye NOT at exit pupil of TS The image of the ent. pupil of the eye through the eye piece becomes the ent. pupil for the TS The objective of the TS becomes the field stop FOV becomes smaller Fo Exit Pupil TS Ent. Pupil Eye Object OBJ Field stop EYP Eye

39 Keplerian telescope: What if Ent. pupil of eye NOT at exit pupil of TS? Objective limits field Unmagnified Camera close to TS exit pupil Camera increasingly farther behind TS

40 Keplerian TS w/ rotated eye: Exit pupil of TS not coincident w/ eye s entrance pupil Jack in the box effect Object seen with axial view disappears with eye rotation (Now you see it, now you don t!) Object OBJ Ent.pupil Fo EYP Exit Pupil TS Entrance pupil of rotated eye Center of rotation of eye

41 Keplerian TS w/ rotated eye: Exit pupil of TS at eye s center of rotation (CR) for best field of view (FOV) When exit pupil of TS at CR, FOV is maintained for rotated eye Reduces jack in the box effect upon eye rotation Object OBJ Ent.pupil Fo EYP Exit Pupil TS Center of rotation of eye (CR)

42 Stops in a Galilean TS f o f e = +30mm f o ' = +50 mm f e = +20 mm Wide range for eye to move behind TS and still see something OBJ is ent. pupil for TS alone but never when TS used w/ eye F o Fo' OBJ EYP Image of OBJ is exit pupil for TS alone but never when TS used w/ eye. Can t make this image coincident with ent. pupil of the eye. This makes it easier for older patients to use. Used w/ eye, OBJ becomes field stop. Reducing the diam. of objective does not reduce brightness, it reduces field of view

43 Galilean TS Brightness and field of view Brightness Exit pupil inside TS Brightness dependent on: Patient s entrance pupil diameter, not the objective diameter Distance from eyepiece to patient s entrance pupil Magnification of TS Field of view is limited by: Objective diameter Distance from eyepiece to patient s entrance pupil

44 Keplerian telescopes field of view FOV is limited by field stop inside the TS located near field lens of eyepiece Image field of view (IFOV) 50 deg for eyepieces used in most LV telescopes FOV is NOT dependent on objective diameter Object field of view (OFOV) for afocal setting OFOV 50 deg/magnification of TS Example: 5x TS: OFOV 50/5 = 10 deg Galilean TS: Field of view 1/3-1/2 that of Keplerian

45 Object (true) and image (apparent) fields of view (FOV) Eyepieces used in most TS used in low vision have an apparent FOV 50 o (Bailey et al) 5X TS Step 2: Object FOV = 50/5 = 10 o Step 1: Image FOV 50 o for eyepieces used in LV TSs

46 Comparison of Galilean and Keplerian telescopes Assume comparable lens power magnitudes Galilean TS Keplerian TS Magnifications 4x All powers (usually no higher than 8X for LV) Length Shorter Longer Weight Lighter Heavier Ease of aiming Easier More difficult Cost Less expensive More expensive Exit pupil Inside TS Behind TS Field of view Smaller Larger

47 Accounting for refractive error w/ TS Use TS over refractive error correction Spectacle lenses Advantage Astigmatism can be corrrected Disadvantage Almost certainly reduced field of view due to TS exit pupil likely not coincident with eye s entrance pupil Contact lenses Spectacle correction incorporated into eyepiece Most commonly done in spectacle mounted TSs Focus the TS by changing separation between objective and eyepiece Lengthen for hyperopia, for either Keplerian or Galilean Shorten for myopia, for either Keplerian or Galilean

48 Altering TS length to focus for uncorrected hyperopia Need converging light emerging from eyepiece AND therefore less divergence entering the eyepiece Move Eyepiece farther from the image from OBJ, located at Reduces the divergence entering EYP Results in convergence leaving EYP Distant object Entering OBJ vergence = L = 0 EYP Emerging vergence = L = 0 Initial afocal setting parallel in, parallel out

49 Lengthen TS for hyperopia - Keplerian Distant object EYP (EYP moved farther, from OBJ) Keplerian TS Entering OBJ vergence = L = 0 Reduced divergence Emerging convergence NOT Afocal Distant object

50 Lengthen TS for hyperopia - Galilean Afocal location (EYP moved farther from OBJ) ' Galilean TS NOT Afocal OBJ Increased convergence EYP Convergent exiting rays

51 Shorten TS for myopia Keplerian Need diverging light emerging from eyepiece to compensate for myopia Move eyepiece closer to the image from OBJ, located at Increases the divergence entering EYP Results in divergence leaving EYP Distant object (EYP moved closer to OBJ) F o EYP Keplerian TS Entering OBJ vergence = L = 0 Increased divergence Emerging divergence NOT Afocal Distant object

52 Shorten TS for myopia Galilean Need diverging light emerging from eyepiece So, must move eyepiece closer to objective, farther from the image from OBJ, located at Reduces the convergence entering EYP Results in divergence leaving EYP (EYP moved closer to OBJ) in afocal location ' Galilean TS OBJ Reduced convergence EYP Divergent exiting rays

53 Examples Uncorrected 5 D hyperope focuses a 4X Keplerian TS (+20D, +80D) on a distant object. Find angular magnification of newly focused TS.

54 Time out for an optical twist Consider a real object placed 10 cm from +12 D lens. Where is the image? Normal approach: L = L + F That is, (Vergence out) = (Vergence in) + (Change in vergence) L = 1/l = 1/(-0.10 m) = -10 D L = L + F = -10D +12D = +2D l = 1/L = 1/(+2D) = +0.5 m = +50 cm Q Object l = -10cm Entering vergence = L = 1/l = 1/-0.1m = -10D F = +12 D l' = +50cm Exiting vergence = L = L + F = -10D +12D = +2 D Image Q

55 Time out for an optical twist Note that, since F = L L, F has 2 components, -L and L (similar to F = F 1 +F 2 ) Q Object F 1 = -L neutralizes the entering vergence, L Rays leaving this hypothetical component are parallel, with Vergence = 0 F 2 = L creates the exiting vergence, L l = -10cm F = +12 D -L L L = -10D L = +2 D Parallel rays, 0 vergence Image Q 2 components of the lens: F = -L + L (= F 1 +F 2 ) F 1 = -L = -(-10D)=+10D F 2 = L = +2D So we maintain F = +10D +2D = +12D

56 This approach is helpful for calculating M A when the length of the TS has been altered to: Correct for ametropia OR Focus on a nearby object

57 5 D hyperope, 4X Keplerian TS (+20D, +80D) Find M for focused TS. Ametropia correction: Rx, with zero vergence entering it Rx = +5D Remaining power in F E : Has zero vergence leaving it Makes it a new eyepiece, NE NE = - Rx = +80D -(+5)= +75D Divide into 2 components M = -NE/ = -(+75D)/(+20D) = -3.8X A bit less than original -4X Distant object +20D =+80D NE =+75D Rx=+5D,F NE Keplerian TS +5D vergence 0 vergence

58 5D myope focusing Keplerian Same 4x (+20D,+80D) Keplerian TS, 5D myope Rx = -5D NE = Rx = +80 (-5D) = +85D M = -NE/ = -(+85D)/(+20D) = -4.2X Distant object +20D =+80D Rx=-5D NE =+85D,F NE 0 vergence -5D vergence

59 Galilean TS 4X, +20D:-80D Galilean TS, 5D hyperope Rx = +5D NE = Rx = -80 (+5D) = -85D M = -NE/ = -(-85D)/(+20D) = +4.2X 4X, +20D:-80D Galilean TS, 5D myope Rx = -5D NE = Rx = -80 (-5D) = -75D M = -NE/ = -(-75D)/(+20D) = +3.8X Summary of effect of focusing the TS to compensate for ametropia Borrowing power of same sign as eyepiece reduces NE and reduces M A Borrowing power of sign opposite to eyepiece increases NE and increases M A

60 Distant object Using a TS to view nearby object Vergence amplification Assume 4x TS Afocal setting Distant object Entering Obj vergence = L = 0 Eyep Emerging vergence = L = 0 Below: Object moved from to 40 cm; image from moves closer to EP, away from Image moves l = -40 cm Q Afocal setting Nearby object Entering vergence = L = 1/l = -2.5D Q Increased divergence Emerging vergence = L M 2 L =(4) 2 (-2.5D) = -40D!

61 Example - Vergence amplification Afocal TS used to view a nearby object without modification Emerging vergence (Entering vergence) (Magnification of TS) 2 L = L x M 2 Example: 4X TS used to view page 40 cm away (l = m) L = (100/(-0.40m) = -2.5 D. L -2.5 D (4) 2 = -40D!! Moral Don t try to use a telescope to view nearby object without modifying it so it s NOT AFOCAL.

62 Add a reading cap Adjust the length of the TS Methods to focus a TS on a nearby object

63 Method 1 to focus nearby object: Add a reading cap Plus lens to neutralize the entering divergence Object F RC f RC = -40 cm Entering vergence = -2.50D F RC L = 0 4x TS, still afocal Emerging vergence = L = 0 Afocal TS with reading cap Nearby object F RC = -1/(-0.4m) = D Equivalent power = (F RC ) x (M A ) = (2.5D) x (4) = D Same retinal image size as using a +10 add BUT working distance is 40 cm instead of 10 cm with the add.

64 Method 2 to focus nearby object: Adjust TS length Increase the separation between the objective and eyepiece to focus near object For both Galilean and Keplerian Divide the objective power,, into 2 components Reading cap power, RC, to neutralize the divergence from the nearby object. Remainder of, which will serve as a new objective, NO NO = - RC

65 Method 2 to focus nearby object: Adjust TS length Increase the separation between the objective and eyepiece to focus near object Q l = -40 cm Increase length Nearby object Entering vergence = L = 1/l = -2.5D Q Increased divergence Emerging vergence = 0

66 Method 2 to focus nearby object: Lengthen TS Plus lens to neutralize the entering divergence Object f RC = -20 cm RC NO 4.0x TS, +20/+80 F NO TS lengthened Nearby object F RC Entering vergence = -5.00D L = 0 = +20 D Emerging vergence = L = 0 RC = -1/(-0.2m) = +5.0 D NO = +20D (+5D) = +15D M A = - /NO=-80/15 = -5.3X Equivalent power = (F RC ) x (M A ) = (5D) x (5.3) = +26.3D Same retinal image size as using a add BUT working distance is 20 cm instead of 3.8 cm with the add.

67 Reading w/ near TS vs comparable spectacle add Longer working distance with TS Smaller field of view with TS Shorter depth of field with TS

68 Prescribing considerations Predicting magnification needed If 20/40 vision is the goal, and patient has 20/100: How many X bigger does 20/40 need to become to give same retinal image size as 20/100? 100/40 = 2.5X TS

69 Measuring M A Direct comparison View repeating pattern, one eye using TS, other eye no TS No TS Through TS 4X TS Entrance pupil/exit pupil ratio as discussed earlier

70 Other descriptions of telescopes Hand held vs spectacle mount Fixed spectacle mount vs clip on Bioptic vs full diameter Monocular vs binocular

71 Other applications of TS Focometer (In-focus) 1X Keplerian TS Calibrated to estimate refractive error Where electricity may not be readily available

72 Other applications of TS Biomicroscope Galilean TS to change magnification

73 Lensometer Other applications of TS A simple lensmeter cross sectional view. 1 Adjustable eyepiece 2 Reticle 3 Objective lens 4 Keplerian telescope 5 Lens holder 6 Unknown lens 7 Standard lens 8 Illuminated target 9 Light source 10 Collimator 11 Angle adjustment lever 12 Power drum (+20 and -20 Diopters) 13 Prism scale knob Eyepiece Reticle Keplerian TS Objective of TS

74 Other applications of TS Emmetropia Spectacle magnification FP eye at infinity Model ametropia as an error creating lens (ECL) in the anterior segment of the emmetropic eye Creates a far point for the eye at the ECL focal point (F ECL ) Correct with a spectacle lens in the spectacle plane with its focal point at the far point of the ametropic eye (that is also F ECL ) Creates reverse Galilean TS effect (minification, as expected with minus spec. lens) F ECL FP eye F ECL FP eye F sp Uncorrected myopia (emmetropia w/ plus error creating lens) F sp (< f ECL ) F sp > F ECL f ECL F sp F ECL +Emmetropia F ECL Reverse Gal. TS Corrected myopia

75 Thank you!