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1/29/16 UNDERSTANDING LOW VISION TELESCOPES Applications for Telescopes in Low Vision Basic and Advanced Observation tasks from audience Theater Ballet Movies Sports Classroom, Public speakers TV in communal environments Ian L Bailey OD, MS, DSc, FCOptom, FAAO School of Optometry General tasks Scenery University of California, Berkeley Faces Cars [email protected] McDonalds Menu Computer screens Mobility tasks Top shelf items Traffic signals Street signs Please silence all mobile devices. Bus numbers, airport signs Unauthorized recording of this Building directories, wall signs session is prohibited. Checking traffic Choices For the Clinician Course Outline or the Patient Review of basic theory Optical Factors Afocal telescopes Magnification Focal telescopes for ametropia or close focus Field size Exit pupil size or entrance pupil for stars Apertures and Stops Adjustable focus/fixed focus Image brightness Range of focusing (for near and ametropia) Field of View and Field of Fixation Can you include astigmatic Rx ? Design Features Image quality Binocular/Monocular Vergence amplification Lens Coatings Hand-held /Head mounted If head mounted Bi-optic ? Practical implications Practical Considerations Tripod/monopod Checking magnification Eye-cup, Objective shroud Measuring BVP Cost Durability Neck, wrist strap, handle Fitting bioptic telescopes Portability (weight/bulk/holder) Influenced by frequency of use Ease of use (mechanical ergonomics) (Protracted, Intermittent, Occasional) Emerging technologies zoom, autofocus, video Cosmesis (conspicuity and perceived acceptability) How do afocal telescopes work? Parallel rays in gives parallel rays out GALILEAN TELESCOPES GALILEAN TELESCOPE Objective Pobj (+/-) A converging element (Convex lens, Concave mirror) P forms a real inverted image. oc Weak objective- long focal length - larger inverted image w w w' Ocular or Eyepiece I Objective’s image must be at primary focal plane of ocular Stronger ocular - short focal length - large image (infinity) f'obj f oc Bailey AAO 2016 1 1/29/16 Image Inversion in Keplerian telescopes KEPLERIAN TELESCOPES KEPLERIAN TELESCOPE Pobj (+/+) Poc w w' w I w' Pechan-Schmidt Porro Prism System Roof Prism System pair of right-angled prisms A Prism A 112.5-45-22.5 f' Prism B 45-62.5-62.5 obj f oc Total internal reflection with 45-90-45 roof so no mirrored surfaces Mirrored surface at 45 deg 45-90-45 45-90-45 Comparing Galilean and Keplerian FOUR BASIC TELESCOPE FORMULAE GALILEAN KEPLERIAN The two obvious relationships Optical path length Short Long Ratio Ocular / Objective Mts = - Poc/ Pobj Image Erect (M=+ve) Inverted (M= -ve) Prisms No Yes Makes it terrestrial d = (1 / Pobj) + (1 / Poc) Sum of focal lengths Ocular Single lens 2 or more lenses Optical surfaces 4 10 or more Two similar formulae (similar to spectacle magnification formula) Exit pupil inside outside M = 1 / (1 - dP ) ts obj Field of view smaller larger Field limits tapered sharp outline M = 1 - d P ts oc Image quality poorer better EQUIVALENT VIEWING DISTANCE 6.3cm AFOCAL TELESCOPES 12.5cm25cm 50cm 2X EVD=12.5cm 100cm AFOCAL iF Parallel rays in give Parallel Rays out EVD=25cm 4X Afocal telescopes have some mathema3cally sweet proper3es EVD=6.3cm EVD=50cm EVD=12.5cm Usually telescopes not quite afocal Objects not at infinity 8X Pa3ents o?en do not want or demand image at infinity EVD=3.2cm EVD=25cm EVD=6.3cm EVD = Viewing distance Enlargement ratio EVD=12.5cm Bailey AAO 2016 2 1/29/16 Adapting Afocal Telescopes (a) POWER CHANGE AT OCULAR for Ametropia Simple and intuitive Hold afocal telescope against own spectacle lens Assume object at infinity OR What can you change? Change ocular lens by adding spectacle Rx (a) OCULAR Place ocular against spec Rx OR Change ocular to include spec Rx Magnification gain = magnification of original telescope (b) LENGTH Change length, changes exit vergence Total magnification = (Spectacle mag) (Telescope mag) No differences for Galilean/Keplerian (c) OBJECTIVE Low Powered Lens Cap OR power change at objective changes exit vergence RARELY USED EVD = viewing distance / Mts FOR HYPEROPE Increase length (b) CHANGE LENGTH Re-assign PLUS power from ocular to provide Rx. Changing length, changes exiting vergence Keplerian telescope Borrow plus from ocular Weaker ocular, longer TS Increasing length adds plus (HYPEROPE) Reduced magnification Also increase length to focus for near (adding plus) Galilean telescope Borrow plus from ocular Decreasing length adds minus (MYOPE) Stronger ocular, longer TS Increased magnification Be able to calculate TS length and Mts FOR MYOPE Decrease length TELESCOPES FOR NEAR VISION Re-assign MINUS power from ocular to provide Rx. 1 Afocal TS with a cap Keplerian telescope EVD = u/M = f /M Borrow minus from ocular ts cap ts Stronger ocular, shorter TS 2. Adjust TS length of afocal telescope Increased magnification EVD = (u/M ) – f EVD ≈ u/Mts ts oc Where foc = focal length of ocular (usually 1-2 cm) Galilean telescope Borrow minus from ocular 3. Afocal telescope over a high add Weaker ocular, shorter TS Rarely used Reduced magnification EVD = Mts . fadd Working distance = M2 f - dM add ts System gives low magnification Long EVD and much longer WD Be able to calculate TS length and Mts Bailey AAO 2016 3 1/29/16 Increasing length Labeling Telescopes a 4x12 TS focused for 20 cm Increase length to 4x12 Monocular telescope M= -100/25 = -4x Two numbers “add plus” for +25 D mm near vision focus. +100 D Magnification x Objective diameter Manufacturers never state negative magnification for Keplerian TS’s 4 cm 1 cm Tube length = 5 cm when afocal 4x12 Effectively borrow is a 4x TS, with objective 12 mm in diameter +5D from objective Adjusted to focus on 20 cm Now system is like a 5x TS with a +5D cap M= -100/20 = -5x Light diverging +20 D 10x50 System behaves like from 20cm +100 D is a 10x TS with objective 50 mm in diameter an afocal telescope 5 cm with a cap on the 1 cm +5D Tube length now 6 cm objective EVD = 20 cm/5x = 4 cm EVP = 25D EXIT PUPILS OBJECTIVE EXIT PUPIL OF KEPLERIAN TELESCOPE Aobj = diam Small images oF ObjecMve lens EYEPIECE A = diam oc Located quite close to eyepiece lens A'obj = Aobj / M ts Keplerian telescopes ( Exit pupil outside TS) Galilean telescopes ( Exit pupil outside TS) Relevant to Image Brightness EXIT PUPIL = image of objective fobj ' foc d Relevant to Field oF View - d / M ts Can help understand imaging by telescopes Exit pupil is a real image suspended in space An important reFerence point Its size is Aobj / M ts It is located d / Mts from the eyepiece lens Can be used to determine magnificaon oF TS OBJECTIVE EXIT PUPIL OF GALILEAN TELESCOPE Image Brightness and Telescopes A = diam obj EYEPIECE A' = A / M obj obj ts A = diam oc REFLECTIONS AND ABSORPTION F All telescopes reduce brightness of real objects EXIT PUPIL = image of objective Light loss (about 15-40%) from reflections f f ' oc from internal optical surfaces obj d Keplerian more light loss - d / M ts More surfaces (compound eyepiece and prisms) Surface coatings reduce light loss Exit pupil is a virtual image inside telescope Its size is A / M obj ts BUT It is located d / M from the eyepiece lens ts TELESCOPES ENHANCE BRIGHTNESS OF POINT SOURCES (STARS) Bailey AAO 2016 4 1/29/16 STARS OR POINT SOURCES Bottom line on brightness Retinal image is smaller than a receptor diameter For Point Sources As the eye gets closer to a point source, the pupil becomes larger in angular size and captures more light from the point. The size of the image of the point is NOT changed. FOR POINT SOURCES Entrance pupil determines brightness Image brightness determined by the area of light capture Inverse square rule for point sources Either TS objective OR M times eye pupil, 2 (whichever is smaller) Image illuminance ∝ 1 / d FOR EXTENDED SOURCES Image brightness determined by size of beam to enter eye For extended sources (large objects) Either eye pupil OR exit pupil of TS, Object does not get brighter (whichever is smaller) Retinal image of object gets larger, but average retinal illuminance remains the same All images from the system are FIELD ASPECT RATIOS within the Image Field Cone IFAR = 10 cm/30 cm Image Field Aspect Ratio (IFAR) Is the ratio of the diameter of FoV = 0.33 = 19° 20 cm at 60 cm Field limiter image space aperture that limits the field 10 cm diameter to its distance from the eye point. Aperture in a card Object Field Aspect Ratio (OFAR) E FoV 5 cm at 15 cm Is the ratio of the diameter of object space aperture that limits the field to its distance from the object space representation of the eye point Eye-to-aperture For Telescopes, IFAR = M (OFAR) = 30 cm Field of View for simple Rule of thumb for Galilean and Keplerian telescopes Fields of View of Telescopes Keplerian Keplerian telescopes (Usually IFAR ≈1) IFAR = A2 / z Keplerian or IFAR = A2 /(d/M) Field limitation by Ocular lens FoV ≈ EVD (or field lens?) Ocular lens subtends a large angle at the eye Galilean Telescopes (Usually IFAR = 1/Mts) Galilean FoV ≈ EVD / Mts Field limitation by image of objective (exit pupil of TS) Depth oF Field oF Telescopes TS exit pupil is small 2 and remote. Thus DoF≈EVD Galilean subtends a small angle at the eye IFAR = (A1 /M) / (z + d/M) 4x12 TS with +5.00D cap EVD = (20 cm / 4) = 5cm = 0.05m DoF ≈ (0.05)2 = 0.0025 m = 2.5 mm Bailey AAO 2016 5 1/29/16 Field of Fixation is smaller than Field of View Imaging through afocal telescopes finite object distances Field of View Extent of peripheral vision during central fixation Field restricting aperture and its distance from the
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