Lecture 10 - Telescopic magnification/adapting for telescopes

Question 1

Telescopic magnification:

Answer 1

• Telescopic magnification is an optical method of magnification, which is more versatile than a plus lens because the magnification can be produced at any viewing distance:
- Distance (street signs, bus numbers, blackboard, theatre)
- Intermediate (playing cards, music, TV, computer)
- Near (reading, writing)
• Telescopes can be hand-held (for spotting) or spectacle mounted, but it is rarely possible to wear them constantly or whilst mobile.

Question 2

General Formulae for telescopes:

Answer 2

• M = - (Fe/Fo)

• t = f’E + f’o

Question 3

Types of telescopes (optical principle):

Answer 3

• Astronomical (Keplerian) telescope in normal adjustment:
• Optical System of (Galilean) telescope in normal adjustment:

Question 4

Astronomical (keplerian) telescope in normal afjustment:

Answer 4

• Fe and Fo positive
• M negative, image inverted
• prism/mirror erecting system required
• both f’e & fo positive so telescope long
• prism allows folding of light path to reduce length (Figure 22)

Question 5

Erecticting systems:

Answer 5

• Astronomical telescopes produce inverted images.
• Terrestrial telescopes are astronomical telescopes which incorporate an erecting system, for example Porro Prisms
(a). Note that the prisms invert the image laterally and vertically.
(b) “Folding” the light path considerably shortens the length of a telescope.

Question 6

Optical System of Galilean telescope in normal adjustment:

Answer 6

• FE negative, Fo positive
• M positive so image erect - (no erecting system required)
• one focal length negative -> short system length

Question 7

Telescopic comparison: Galilean vs Keplerian

Answer 7

Galilean
• Weight: Lighter
• Length: Shorter
• Exit pupil: Inside
• Image: Erect
• Magnification: Low up to 4x
• Field of view: Smaller
• Image quality: poorer
• Cost: lower

Keplerian
• Weight: Heavier
• Length: Longer
• Exit pupil: Outside
• Image: Inverted
• Magnification: Low and high, up to 10x+
• Field of view: Larger
• Image quality: Better
• Cost: Higher

Question 8

Labelling of telescopes examples:

Answer 8

Galilean telescope
Examples:
Magnification: 2.2 x
Weight: 16 grams
Visual Field: 250m/1000 m

Magnification: 3x
Lens: Monocular
Field of View: 12.5°
Working Distance: 45-200

Sometimes telescopes are labelled as follows: 8 X40
- First number = magnification, second number is diameter of objective lens

Question 9

What is the Exit pupil:

Answer 9

• Exit pupil (XP) is the image of the objective lens seen through the eyepiece. All rays entering the objective lens pass through the exit pupil. Therefore the size of the XP is an important factor in defining the field and the brightness of the image. The size of the exit pupil can be determined by direct measurement or calculation. The question then is whether the telescopes XP should match the size of the patient’s pupil or be bigger or smaller.

Question 10

Position of exit pupil:

Answer 10

• astronomical: EP behind Fe -> patient’s eye can get close to EP, see Figure 24
• Galilean: EP between Fo and Fe -> greater distance between EP and eye

Question 11

Size of exit pupil

Answer 11

diameter of exit pupil = diameter of objective lens/magnification of telescope

Question 12

modifiable factors affecting a telescope’s field of view:

Answer 12

• Magnification - use minimum power
• vertex distance
- 5mm = closest distance without specs:
- 20mm = likely with specs and rubber eyecup
• object distance
- not practical to change this
• obiective diameter
- telescope becomes heavier and more difficult to handle

Question 13

How can field be optimised when using telescope?

Answer 13

• Match size of exit pupil to the patient’s pupil,
- if the alignment slips part of field will go dark.
• Therefore better if exit pupil > patient’s pupil, which allows some misalignment, but obviously means some loss of field.
• Calculations of the field of view do not accurately reflect actual patient experience, because the patient’s pupil is the limiting aperture rather than the telescope’s objective lens.
• The effect of aberrations is also not accounted for by FoV calculations based on Gaussian optics.

Question 14

Focal telescopes:

Answer 14

The formulae derived above relate to focal systems, but
• A telescope can be modified for different object distances and to correct the patient’s refractive error.
• Modifying or focusing the telescope may alter the lens positons/powers and affect the telescope’s magnification.
• This applies to both astronomical and Galilean telescopes. The first question is what would happen if patient used a telescope in normal adjustment to view a near object.

Question 15

Adapting telescopes for near and intermediate viewing methods

Answer 15

1. full correction for viewing distance over objective (Fo)
2. increased correction for viewing distance over eyepiece (Fe)
3. increasing the separation of Fe and Fo

Question 16

Method 1. Full correction for viewing distance over objective (Fo)

Answer 16

• Plus lens in front of objective lens - “reading cap”
• Telescope + reading cap = “telemicroscope”
• Used particularly with Galilean systems
• Frc has a focal length equal to the required working distance
•Parallel light enters telescope so magnification as labelled

Question 17

Total magnification for telemicroscope:

Answer 17

• MTOTAL = MTEL X MRC
• MRc = FRC/4
(as for all plus lenses)

Question 18

Why use tele-microscope instead of simple spec-mounted plus lens? Practical considerations? Measuring power of the reading cap?

Answer 18

• Working space is greater with telemicroscope

Question 19

Practical considerations of using telemicroscope over simple spec-mounted plus lens?

Answer 19

• even if working space is 2x larger, not useful unless at least 5cm increase
• increased working space makes binocular viewing more practical
• need to be able to angle telescope tubes appropriately (convergence)
• overall working distance increased by length of telescope (minor point)

Question 20

Measuring power of reading cap: telemicroscope over simple spec-mounted plus lens?

Answer 20

• If separate from telescope, measure equivalent power by usual technique
Moderate power, so back vertex power with focimeter acceptable
If incorporated, measure front vertex power of whole device with focimeter
Also gives working distance; fRc = 1/FR

Question 21

Method 2. Increased correction for viewing distance over eyepiece (Fe)

Answer 21

• Not a practical method unless patient already has high-powered reading add for other purpose
• Magnification difficult to calculate unless all system parameters known

Question 22

Method 3: Increasing the separation of Fe and Fo (focusing)

Answer 22

• A practical method, but more difficult in spec-mounting
- can become “front-heavy” as tube length increases
- difficult to angle correctly if binocular
• More common in astronomical telescope
- usually hand-held anyway
- image quality better maintained

Question 23

Conclusion for using telemicroscopes:

Answer 23

• working distances (>25cm) better to refocus a telescope than to add a reading cap, as this will provide higher magnification.
• Practical limitations include the increase in telescope length. The closest possible focusing distance corresponds to the LONGEST position of telescope (t=max) so there are practical/mechanical limitations and sometimes the tubes cannot expand far enough.

Question 24

Why use telescopes for near vision?

Answer 24

The major reason for using telescopes for near tasks is the increase in working space compared to magnifiers. (2x telescope increases by factor 2; 3x telescope increases by factor 3 etc.). This is usually needed for manipulative tasks. but: The field of view is very small.