LV: Types of Telescope

Basic types

• Hand held
• Clip on
• Spectacle mounted
• Monocular versus binoc
• Focus/Afocal

Specials

• Autofocus
• CL telescope
• IOL lens scopes
• BTLT - Behind the lens telescopes. These offer cosmetic adv but great care must be taken obvs. Increased risk of eye injury if the patient bumps into something while wearing them. Also v expensive
• Bioptic - for px who fulfil certain requirements driving with bioptics is legal in some US states, not here. Px can resolve fine detail like road signs

Contact Lens Telescopes

• These use a galilean system where the obj lens is a high plus spec lens and the eyepiece is a high powered -ve CL. The vertex dist of specs is equal to the sum of the focal lengths (length of the telescope)
• The FOV is better than with a conventional telescope cos the exit pupil is really close to the eye but it also depends on the objective diameter (use a blended aspheric to avoid a ring scotoma)
• Has many practical and cosmetic disadvantages though so is rarely used.
• EG a +20DS spec lens and a -40DS contact lens. Px is emmetropic.

The fitting of

• check that normal scope improves VA as expected
• Check nystagmat for oscillopsia
• Fit CL, maximise vd of trial frame, perform over-refraction
• CL must be stable
• Vergence amplification means separate reading specs are required
• Account for uncorrected ametropia - +10D hypermetrope with -30CL effective eyepiece is -40 and -10 myope with -30 CL effective eyepiece is -20.

Advantages of

• In theory px could drive under uk law if visual requirements were met
• Can get acuity much better than expected in congenital nystagmus
• IOL could be used instead of CL giving a longer vd so better magnification but IOL can't be changed if acuity worsens

Disadvantages of

• Low magnification so only works for moderate acuity loss
• Patient has to be adapted to CL wear & it's difficult to insert contact lenses
• Need to wear the system regularly for long periods
• Adaptation to spatial distortion required
• Poor cosmesis with high vd and big fat plus lenses
  

Telescopes: Depth of Field

If you do calculations it appears that plus lenses and telescopes have the same depth of field, but px feel it to be less in telescopes. This could be because the dept of focus for the telescope represents a smaller portion of the working space. Anyway here are some more lovely calculations

Ok, the px has 0.5D depth of focus. What change in incident vergence or object distance could the px tolerate:

a. With a plus lens mag of 10D

f = 10cm if obj at focal point

let emergent vergence = +0.5D
L' = L+F = 0.5-10 = -9.5cm

let emergence vergence = -0.5D
L' = L+F = -0.5-10 = -10.5cm

So overall there's a 1cm range

b. With a 2.5x scope with a +4.00

Emergent vergence Ltel = L'tel/M2 = +/-0.5/2.52 = +/- 0.08m

The incident vergence at the reading cap is of course -4D to match up with it so

delta l = (1 / -4D+0.08D) - (1 / -4D + 0.08D) = (1 / -3.92) - (1 / -4.08) = 1cm

NB Aberrations may also have an effect on the depth of field.

NB2 Changing the obj posn can alter the vergence of light entering the eye. This could create a refractive correction for spherical ametropia

• Move obj closer to magnifier: light divergent leaving magnifier so uncorrected myopes need to hold material closer
• V.V. ie uncorrected hyperopes need to hold material further away
• The effect is similar for both plus lenses and telescopes but because of vergence amplification the effects will be much more severe for telescopes
  

LV: Compensating Telescopes for Ametropia

Again there are three methods for this

1. Full correction for refractive error behind eyepiece

This is the simplest method in which the telescope is clipped onto or held over the spec correction. You could also fit a correcting lens into a holder behind the eyepiece if required. This method doesn't have any effect on the magnification of the system because the telescope is still afocal (unmodified).

2. Partial correction for Rx over objective lens

This achieves some divergence or convergence of light entering the telescope which is then amplified by the telescope to give the correct amount. This is complex to work out and rarely attempted.

3. HERE WE GO MORE F'IN CALCULATIONS: Changing the separation of Fe and Fo

• Shorten the scope to correct myopia and lengthen for hypermetropia - how much depends on Rx
• Changing the length has an effect on magnification

Astro Example

Work out the magnification and length of a 3x astro (Fe +60, Fo +20) used by a -10.00 myope with the correction behind the eyepiece. NB With a myope you want divergent light coming out of the eyepiece which can then bend into the patient's eye thru the specs

a. The magnification is as for an emmetropic user as the telescope is afocal so = -Fe/Fo = -3x
b. t = fo' + fe' = 50mm + 16.7mm = 66.7mm

Ok that was easy, but what about if the guy was uncorrected and the telescope was focussed to compensate?

t = fo' + fe' = 1/20 + 1/60-(-10) = 64mm

it's like a part of the Fe power has been borrowed to correct the ametropia leaving it as +70D
So to correct for myopia you need to decrease the sep between the lenses w/Astro
And to correct for hyperopia you need to increase the sep between the lenses w/Astro
the Fe in that case will go down to +50D and the length will increase to 70mm.

Galilean Example

3x Fe = -60, Fo = +20 fixed for -10 myope

t = fe' + fo' = 1/20 + 1/(-60+10) = 0.05 - 0.02 = 0.03m = 30mm
Mtel = Fe / Fo = 50/20 = -2.5x

Conclusion

Myopia

• Higher mag with focussing astro
  
• Increase length of astro telescope to correct
• Higher mag with correction behind eyepiece for Galilean
• Decrease length of Gal to correct

Hypermetropia

• Higher mag with corr.behind eyepiece with astro
• Decrease length of astro to correct
• Higher mag with focussing Gal
• Increase length of Gal to correct

These egs used large ametropias so effect less pronounced usually. Any big cyls >2.00 will have to be corrected behind the eyepiece. Removing spec correction = shorter v.d. and wider field of view but if the scope is going to be used for spotting then it may not be practical to remove specs. Telescopes are mainly used for near vision due to the increase in working space which is usually needed for manipulative tasks like writing or sewing or some ting. The problem is the fov is far smaller so this counteracts that whole thing a bit.

LV: Focal Telescopes

These telescopes can be modified for different object distances and to correct ametropia. Both Gal and Astro.

Vergence Amplification (Freid's Formula)

Vergence entering telescope L = 1 / l

Vergence leaving L' = M2L / 1-t M L where M is the magnification and t the tube length

For practical purposes t is very small compared to l so we can simplify to L' = M2L

eg How much accomm required when a patient uses a 3x telescope for reading at 25cm?

L' = M2L = 3 squared x 4 = 36D - would have to accomm 36D which is too much even for kids

Adapting telescopes for near and intermediate viewing

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

1 Full correction for viewing distance over obj

• 'Reading cap' over objective lens. Telescope + reading cap = telemicroscope
• Used particularly w/Gal system
• Frc has focal length equal to the required WD
• Parallel light enters telescope and parallel light comes out

Total mag of telemicroscope Mtot = Mtel x Mrc (Mrc = Frc/4)

eg What magnification is achieved when using a telemicroscope w/ 3x telescope and a +4D reading cap?
= 3 x 4/4 = 3x magnification

working space frc = 1/4D = 25cm

So I can see why they use em - to get 3x with a plus lens the working dist would be tiny. Like 8.33 cm. But here it's 25cm which is way more tolerable. Increased working space makes binocular viewing more practical too - that's only possible with about 2.5x with plus lenses, but 5x w/telescopes. You do need to angle the tubes properly though. NB the overall working distance is increased by the length of the telescope too.

2. Increased correction for viewing distance over eyepiece

This isn't a practical method unless the patient already has high-powered reading add for another purpose. Magnification is difficult to calculate.

3. Increasing the separation of Fe and Fo

• A practical method but more difficult in spec mounting - becomes more front heavy as the tube length increases. Difficult to angle if binocular
• More common in astros cos they are hand held usually anyway and the image quality is better maintained

Example

2.5 Gal (Fe = -50D, Fo +20D) focussed for 25cm using a 4D reading cap

Mtel = -Fe/Fo = -(-50)/20 = 2.5x
Frc = 1/l = 1/0.25 = +4.00
Mtotal = Mtel x Mrc = 2.5 x 4/4 = 2.5x

t = f'e + f'o = -0.05 + 0.02 = 30mm

Example 2

2.5x gal focussed for 25cm by changing length so reading cap is 'incorporated' in Objective lens

so t = fo' + fe' = 1/Fo + 1/Fe = 1 /20-(1/0.25) + 1/50 = 0.0625 + (-0.02) = 42.5mm

Mtel = -Fe/Fo = -(-50)/16 = - (-50)/20-(1/0.25) = 3.13x

Frc = 1/working space = 1/0.25 = +4.00

In conclusion higher mag can be achieved by focussing the telescope rather than adding a separate reading cap BUT this causes a large increase in length. Not always practical cos the lens housing cannot expand by this amount and it may make the mounting unstable

Example w/Astro

What are the mag and length of a 3x astro telescope Fe = +60, Fo = +20 focussed for 12.5cm w/reading cap

Mtel = -Fe/Fo = -60/20 = -3x
Frc = 1/working space = 1/0.125 = +8.00D
Mtotal = Mrc x Mtel = 3x2 = 6x
t = fo' + fe' = 1/20 + 1/60 = 66.7mm

Example 2

3x astro focussed for 12.5cm by changing length

Mtel = -Fe/Fo = 60/20-8m = -5x

Frc = 1/0.125 = +8.00D

Mtot = Mtel x Mrc = -5 x (8/4) = 10x
t = fo'+fe' = 1/Fo' + 1/Fe' = (1/20-8) + (1/-60m) = 83.3mm + 16.7 = 100mm

Conclusion

For both astro and gal focusing will always provide higher magnification than a reading cap because Mtel increases when Fo decreases, but there are severe practical limitations re increase in telescope length. NB closest focus distance = longest position of telescope (t=max)

LV: Telescopes!

These are a method of optical magnification which is more versatile than the plus lens.

• Distance, intermediate or near
• Hand held for spotting or spec mounted but rarely worn constantly/whilst mobile

General formula (for afocal telescopes) is M = -Fe / Fo and also t (tube thickness) = fe' + fo'

Two types of telescope - astronomical and galilean

Astronomical

• Both eyepiece and obj lens are +ve, this gives -ve magnification and an inverted image
• Both focal lengths positive so the telescope is long
• Prism erecting system needed too
• Heavier, longer and more expensive than galilean
• Larger field of view and better image quality though
• Exit pupil outside system
• Mag range from low - high. Up to 10x
  

Galilean

• Eyepiece lens is negative and objective lens positive. +ve mag so erect image
• One focal length is negative so the system is shorter
• Lighter, shorter and cheaper than astronomical
• Poorer image quality and small field of view though
• Low magnification only - 4x maximum
• Preferred for spec mounted due to lower weight and shorter length

Labelling

• Magnification 2.2x, 3x etc
• Weight in grams
• Visual field 250m/1000m linear OR eg 12.5 degrees (200 degrees without scope)
• Working distance 45-200cm
• Sometimes written 8 x 40 where first number is mag and second number is diameter of objective lens in mm

Exit Pupil

• This is the image of the objective lens seen through the eyepiece. All of the rays entering the objective lens pass through the exit pupil.
• The exit pupil defines the field and the amount of illumination. These can be determined by direct measurement or calculation. Ideally the patient's pupil should be exactly the same size
• Astros have EP behind Fe so patient's eye can get close to it, with Gal the exit pupil is within the telescope so there's a greater distance between it and the eye

diam of exit pupil = diam of obj lens / magnification of telescope

eg size and location of the exit pupil for a 3x24 gal telescope with an Fo of +10.00D

Fe = -3x10.00 = -30.00

1 / l' = 1 / l + F = 1 / -0.0667 + (-30) = -45

1 / -45 = -22.22cm SO EXIT PUPIL IS 22.22cm IN FRONT OF THE EYEPIECE

24/3 = 8mm SO EXIT PUPIL IS 8mm IN DIAMETER

Factors Affecting Field of View

• 1/Mag - use minimum power - use min until px becomes practiced
• 1/vertex dist - 5mm = smallest dist w/o specs, 20mm = w/specs & eyecup
• Object distance
• Object diameter - but telescope becomes heavier and more difficult to handle

Matching the size of the exit pupil to the px's pupil optimises the field BUT if alignment slips even a tiny bit part of the field will go dark, so in practice it's actually better if the exit pupil is greater than the patient's pupil despite some loss of field as a result - the misalignment is more easily tolerable. Better to measure in practice than calculate as more closely related to px experience.