From Low Vision 1 To Flashcards
Who needs low vision aids and how does magnification help people see.
Purpose of them and 3 ways of increasing retinal image size
Those who can’t resolve retinal image eventhough it is focussed on the retina eg elderly pxs with armd or normal sighted people that need to see fine details eg jewellers
Mag helps people see as it makes the image bigger so there are enough photoreceptors to cover the image. Even w damaged photoreceptors.
Purpose of lva- to increase retinal image size so px can resolve details they cannot without LVA.
-increasing relative object size
-reducing relative viewing distance (simple magnifiers)
-increase angular subtense by optical means (telescope next lec)
Wha is magnification
Ratio of retinal image size. Use object size to find out mag.
M= new retinal image size/old object size
Or old object distance/ new object distance
Old object distance= reciprocal of add (pxs habitual wd) and new object distance is from the focal length of magnifier.
Theta’= angular subtense
(M= theta’/theta (new object size/ old object size= h2/h1)
M=l1/l2= original wd/ new object distance (focal length of magnifier)
Mag varies from person to person, same person wont get samemag. Cant measure retinal iamge size but measure object distance or size to predict mags for individuals. Mag is a combination of increased object size and reduced viewing distance.
increasing object size- larger print
Also what ones reducing viewing distance do
h1= angular subtense of theta
now double object size to h2 = doubles angular subtense
image size doubles as little error, ignored curved as retina is curved
doubling object doubles the retinal image size
magnification= new angular subtense/ old one. New object size/ old So mag1= h2/h1
Halving distance doubles angular subtense doubling retinal image size
Reducing viewing distance so what is total mag
And what must you instruct your pxs to do
subtense doubling retinal image size.
M2= l1/l2. L1=original working distance. L2= focal length of the magnifier, old object distance/ new object distance (The old object distance is a reciprocal of the pxs add so their habitual wd, new from focal length of magnifier) This what simple magnifiers do.
mag is the product of the two, doubling size of object and reducing the viewing distance. So 4 times mag all together as it doubles it for each way.
Instruct px to use them with distance correction and they need to hold it at their focal length away. Old object distance is the users habitual wd so reciprocal of their add or accom they use. Bit of variation as we do have some depth of focus as well. Eg 3D add holding at 33cm etc.
if magnifier not held at focal length the mag would also depend on accom or near add being used as if it isnt held at the focal length we’ll have diverging light coming out of magnifier so you’d either accomodate or use an add. this diverging light would result in smaller and less clear image so need more accom or add to compensate for reduced mag.
Problems with magnifiers and simple magnification nominal mag
Problem w mag- mag marked on magnifier not always mag the px gets. Depends on pxs habitual reading distance, where they hold the magnifier and if theres any near add or accom.
Simple magnifier- nominal magnification-
put number on mag for general idea. Nominal magnification assumes the habitual working distance of everyone is 25cm. Assumes no accom and very small distance to the eye d, assumes magnifier is held at the focal length.
Theta without magnifier, with magnifier and also nominal magnification calculations
Theta without magnifier= h/q assuming small angles. (Angular mag= H is the height of the image formed by the magnifier and q is the distance of the object from the magnifier- remember -ve as in front real object)
Magnifier at focal length from object imaged formed at infinity. Theta’ (angular mag achieved by the magnifier)= h/fm. H is the height and fm is focal length of magnifier which is shorter than habitual working distance as want to bring things closer. As at infinity no extra add or accom so using distance rx.
Magnification= the power of magnifying lens/ power of original reading spectacle add (assumed to be 4)
So the nominal magnification= M=Fm/4. Fm = power of the magnifying lens. 4. So M times 4= power
Putting a simple magnifier closer than the focal length
Closer objects will need add or accom.
The light is diverging so px will need accom or reading add. Image size varies with lens to object distance. Image size varies with lens to eye distance.
If the lens is moved closer to the object this reduces mag due to the magnifier alone and we will need to consider addition/ accom effects on magnification as well.
Another equation for theta
What is the max wd for a magnifier
and also m with Q
Theta’= h’/ (d-l)
maximum mag is when d=0 and accom/addition reduces as d increases.
Max wd for magnifier- focal length. If object held further away than focal length light emerging from magnifier= convergent and the eye would focus that light in front of retina= blurred image if magnifier is further away from focal length.
M= -l’q/l(d-l). Q is the habitual working distance without a magnifier
so mag is dependant on the habitual working distance and the distance from the lens to the eye as well as object distance and image distance
Trade magnification or maximum magnification
some manufacturers define magnification assuming the user is wearing their habitual 4.00D addition to view the image which is also at 25cm. Or viewer must be exerting 4.00D of accom.
Another value manufactures use to mark magnifiers
assumes wearer is wearing reading specs w magnifier held in contact with eye
Habitual and new image distance is 25cm
extra power must be taken into account when calculating lens sytem power
M= Fmag/4+1= Nominal magnification+1
E equivalent power- which F value should we use
what F value should we use- thin lenses all equal but most magnifiers are thick lenses so should use equivalent power.
This takes into account principle planes so principle plane to the principal focus.
Positive bi convex lens- bvp would be greater than equivalent power
can’t measure using foci meter, need to work out surface powers with lens measure and go from there. Manufacturers often quote the bvp so stated mag is higher.
Feq= F1+F2-t/n times F1F2
Or
Fe= Fm+ Fa- d times Fm times Fa
if magnifier is held at the focal length away from the eye then d is the focal length of the magnifier which means that Fe=Fm. Makes sense as no accom or add then
d= separation of the magnifier and spectacle len or eye
Fm= power of the magnifier
Fa= power of the add or accom
Simple magnifier working distance max and min what is Y what is D
What is linear fov
How do get greatest fov
And low power and high power
mag working distance- focal length. If further away then image is blurry as it forms in front of the retina.
Minimum working distance lens to eye- depends on users accomodation as an object inside the focal point will give divergent emerging rays.
Y is linear fov, D is the diameter of lens.
Linear fov= defined as the angle subtended by the lens periphery at the image of the eyes entrance pupil.
To get the greatest fov-
large diameter
as close to eye as possible (d)
lowest power Fm
higher power- smaller diameter as lens diameter is limited by weight or thickness and peripheral aberrations and manufacturing as greater surface curvature.
Aberrations
higher power greater aberrations
high plus lenses- best form lenses usually only minimise aberrations for lenses up to +7.00D
aberrations reduced by using aspheric surfaces and or lens system
Hand magnifiers advantages and disadvantages
illuminated hand held or just hand held
can be used with right and left hand
convenient and familiar
Can be illuminated
lightweight, compact, portable
cheap
eye ego magnifier distance can vary without affecting the magnification if the object is at the first focal point allowing for adjustments in total working distance
disadvantages- long eye to magnifier distances=smaller fov
easily obtainable without instruction so may be using it wrong
need a steady hand
internal illumination can make it too heavy
only one free hand for other tasks unless mounted
Stand magnifiers tell me about h them. Same equation
Why not make them to focal length
Where is the image formed
pxs with unsteady hands, need two hands
height of stand is typically less than the focal length of the lens so emergent light is diverging.
Why not make them to focal length- if sun goes through them paper can catch fire
Px must accomodate or use add for the image distance
this creates a magnifying system made from the combination of the magnifier and reading add or accomodation. Need to make them special glasses just for this often.e
Fe=Fm+Fa-d times Fm times Fa
Mag is also greatest when eye or spec lens is in contact with the lens this requires the highest reading add which increases mag.
The finite image distance means the image formed below the magnifier and user must be corrected or accomodate for this distance so we need to know the reading add needed to neutralise the divergence.
Measuring the exit vergence of stand magnifiers
the telescope is focused on infinity so on a distant object and then its used to observe the image through the magnifier to ensure the image will only be in focus when the emerging rays from the magnifier are parallel.
Trial lenses are added until the image is clear. The exit vergence is opposite to the power of the trial lens. The trial lens power is the power of the reading add needed if the user views the image with the eye close to the magnifier.
Examples of stand mags from lecture
illuminated stand magnifiers, tilt stand magnifiers, easy view hangs around neck and propped against chest- low mag as large lens. Bright field magnifier
advantages and disadvantage os stand mags
stable working distance, advantageous for high power lenses or when px unsteady hands
hands free- useful for low power lenses when plenty of working room under lens eg writing, drawing, crafts etc
can also have built in illumination
disadvantages- need reading add specifically for use with the magnifier. The user must use the magnifier at the correct distance from their eyes to focus.
High powered stand magnifiers dont leave enough room under for tasks to be performed as many have stands that completely surrounds the lens allowing no access beneath and requiring internal illumination if stand not transprent
internal illumination can make stand
1)What are the 3 ways of increasing the retinal image size with low vision aids
increasing object size
reducing viewing distance- needs increased accom/ reading add. If the original working distance is 50cm= 2.00D of add or accom and 2 times mag is needed then the object will have to be moved to 25cm with 4.00D add/ accom. If however the original working distance is 25cm the object will have to be moved to 12.5cm with 8.00D of accommodation or an 8.00D add to give 2 times magnification. Thats a lot they need to focus it there.
increasing angualr subtense by optical means- telescopes
2) How do simple magnifiers work as low vision aids-
Simple magnifiers are high plus lenses which increase the retinal image size by decreasing the working distance at which the near task is performed. The increased retinal image size means the user is able to resolve detail they would not be able to resolve while holding the object at the original working distance.
But you have to compare the situ with the magnifier to the original situ without so we cannot give a magnifier a definitive value for the mag a user will as it depends on users original or habitual working distance and on how the magnifier is used.
If you have someone who reads at 25cm and they want 2 times mag. 25/2= 12.5 halving viewing distance doubles the mag. If using w distance correction this would be equal to the mag marked on the magnifier. they will get that nominal mag. Would need 4.00D accom or add.
If someone reading at 50cm tall and long arms, 2 times mag they would only have to move their wd to 25cm. Original wd 50cm= 2.00D of accom or add
someone w 2.00D add to help them see at 2 times mag= 4.00D
someone with 4.00D add 2 times mag= 8.00D add allows them to focus at 12.5 cm
50cm. If used that same magnifier as 25cm person if they held it at 12.5cm they would get 4.00D magnification whereas other person got 2 times mag. (Or just forget this and doing calculations Nom mag=Fm/4 1/0.08 is 12.5)
3) What is nominal magnification-
what is trade mag
Max and min wd and whats does equivalent power do
Nominal magnification is the value of magnification often marked on simple magnifying lenses. It is the mag we expect if all assumptions are met. The assumptions that nominal mag are based on are that the users habitual wd is 25cm and the magnifier is held at its focal length away from the object.
M=h/q. (2=0.025 as it assumes the habitual working distance is 25cm) assumes magnifier is held at its focal length from the object- no add or accom.
M=1/Fm
trade magnification- assumes that the image is also at 25cm and so the user needs 4.00D accom or add, assumes the spectacle or eye to magnifier distance is 0 so the power of the lens system is the sum of the addition and the magnification.Fm+4/4
So trade mag= Fm/4+1
Equivalent power works out the power relative to the principle plane of the lens system. Reciprocal; pf the distance from that plane to the image. If that distance is greater than the distance from the back vertex to the image then principal power is less than bvp.
Max wd= focal length of the lens.
Min wd= hold it closer magnifier closer to object diverging rays out of mag lens so need to accom. Sot his depends on how much accom user has.
2) Why are stand magnifiers used with an addition whereas handheld magnifiers tend to be used with the distance rx-
stand magnifiers have a height which is less than their focal length which means that light emerging from the magnifier is diverging as the image is closer than infinity. To focus on the image the user will need an addition or needs to accomodate.
Px’s normally instructed to wear their distance rx when using handheld and will be shown where to hold them. They are not expected to know what the focal length of their magnifier is they find it as it will be the only position which gives them a clear image if they have no accomodation.
What do telescopic magnifying systems do, what are they used for and what are the two types
What type of system are there and what does that mean
Telescopic magnifying system change the angular subtense without having to change the working distance.
Used for distant and intermediate tasks as well as near tasks. But small fov means they cannot easily be used when mobile so walking around.
Two types-
astronomical/ keplerian: two positive lenses
Galilean- positive and negative lens
both afocal systems so parallel light comes in and parallel light out
Astronomical and Galilean main difference
Astronomical or keplerian- positive eyepiece negative first foacl length so neg mag inverted image
Galilean- negative eyepiece, positive first focal length so positive mag and upright
Astronomical- if fe is positive d=fo’-fe but fe is neg so — makes a plus so distance increases so longer than astronomical.
Galilean- fe is positive so you minus them
Astronomical how do they work and where do we need the lenses to be for an afocal system
What is fov determined by and whats it like in this telescope
What is the mag equation
Objective: positive lens- has second focal length of 0 fo’ to get parallel light coming out and then the objective forms the image at the second principle focal point. Parallel light always forms image at F’. So we need that image to be at the first principle point so light coming out of the eyepiece will be parallel. So position the eyepiece so its at the first principle focal length away from the image formed by objective= parallel light emerging from telescope.
Keplerian- inverted image, minus sign tells us the image is inverted
fov is determined by the size of exit pupil- exit view is close to the eyepiece in Kepler- closer to eyepiece= better fov. Can get right up to the eyepiece at second principle focal point.
M= theta’/theta. M=-fo’/fe’=-Fe/Fo
assume thin lenses so assume that fo=fo’ and fe=-fe’
positive eyepiece, negative first focal length, neg mag= inverted
Galilean same question. What’s the iamge height and fe’. Explain about fov and let’s talk about distance for both Galilean and astronomical
negative eyepiece, positive first focal length, pos mag= upright.
second lens placed so the image forms at focal point of the eyepiece. Negative eyepiece so the image formed by the objective is at the first principle focal point of the eyepiece.
Image height still negative fe’ is also neg so ends up being the same as astronomical and theta is the same but power of the eyepiece is negative so we end up with a positive mag= upright image.
galilean is shorter than astronomical. The exit pupil is at the second principle focus somewhere inside the telescope so cant pop eye right close to the eyepiece unlike astronomical so smaller fov.
Galilean: d= fo’-fe (fe is positive) first focal length
Astronomical- d= fo’-fe (fe is negative) first focal length
Can you accomodate through your telescope
Telescopes for intermediate or near viewing- two practical solutions
most people may be younger as they are tricky to use so may have accom. May need accom for intermediate or near tasks.
Telescopes for intermediate or near viewing- two practical solutions
-adding full correction for the viewing distance in front of the objective in the form of a reading cap. (Put reading cap over objective- this neutralises divergence from near object so makes rays going into the system parallel again, another lens basically so need to work out mag for lens system )
-Refocusing the telescope by increasing its length (or can refocus telescope by increasing its length though it would no longer be an afocal system if change the length of the telescope)
Near adjustment reading cap
eg incident vergence of -10D can be neutralised by a reading cap of +10D. The resultant mag of the system is now the product of the magnification of the telescope and the reading cap.
Simple magnifier Fm of 25.00D is too big wouldnt want to put in specs. Could put higher add in specs but becomes too heavy and thick. Working distance bit clos as well but telescopic allows you to have larger wds with the same magnification.
Focusing the telescope near adjustment
Need Fe to coincide with Fo’. Work out new separation,
Then use d value in metres with the equation
Feq= Fo +Fe -dFoFe.
Then do Feq/4 as it assumes 25cm wd if wd was different then value to divide it by would be different. (Eg 1/0.25=4)
Telescopes FOV
Mag and objective lens diamter often marked on telescope. 8x20 means 8x mag and 20mm diameter objective.
greatest fov achieved when the pupil of the eye is coincident with the exit pupil which isnt possible w Galilean.
Astronomical- real exit pupil beyond the eyepiece
galilean- virtual exit pupil inside the system
Exit pupil diameter=objective lens diameter/ mag of telescope
Measuring magnification. And what is the exit pupil
the exit pupil is the image of the objective aperture seen from the eyepiece
hold the telescope with eyepiece about 20cm from your eye and point it at a bright target and measure the size of the exit pupil. Measure the diameter of the objective lens. This is often marked on tege telescope with the mag.
Or by comparing a shape image
Prismatic telescope
prisms shorten the telescope and make the image erect. Astronomical things are upside down which isnt good so most these things have prismatic telescope within them that turns everything the right way up.
Prisms also shorten the telescope. Mag now is still Fe/Fo. Still comes out negative value but would gibe it a positive value. Compact and handy. Prismatic monocular attached.
Advantages of telescopic systems
high levels of mag can be achieved at varying wds near distant intermediate.
But small field of view and cannot be used while mobile and object of interest can be difficult to locate.
Examples of telescopic systems
keeler LVA 22 near vision telescope with 5 times mag. Fixed focus. Note convergence
spectacle binoculars- Galilean telescopes. 2.0 x mag.
Distance clear lens= can adjust distance between lenses-> diff wds.
How do telescopes work
Telescopes distant viewing- parallel light into telescopic system and coming back out of it=afocal system- user can use it to view distant objects while wearing their distance rx. Train timetables at a distance etc. not good when mobile as small fov.
What would the lens sep need to be adjusted for to neutralise the accom
you need to move the eyepiece to a spot where it is at its principle focal length away from the image formed by the objective.
For the system on worksheet 1,1c what other method can you use to compensate for the divergence of the emerging rays
Adv and disadv of low vision aids
we can use a reading cap placed over the objective with dioptric power equal and opposite to the initial vergence. This neutralises the initial divergence so we have parallel rays entering the telescope. The telescope can then be left in distance adjustment.
Remember adv disadv of all low vision aids think ab working distance, ease of use, visual field and cost. Talk to px what minimum mag do they need, what wd will they be working at, have they got steady hands, will they be able to use the aid. Instruct them on how to use it and where to hold it, do they need their distance or reading specs. How do they adjust it for diff working distances.
In distance adjustment wha t happens with first principal focus of eyepiece and second principal focus of objective
And for calculations waht do we assume
The first principal focus of the eyepiece fe coincides with the second principal focus of the objective fo’
We assume thin lenses as fe=fe’ and fo=fo’ so when we work out reciprocal of Fe this gives us fe’ which is second principal focal length we just take this as opposite sign as fe=fe’ bc we want first principal focal length so remember Galilean is positive kep is neg so Galilean gets shorter and for kep you do — to get positive so you add it onto the objective focal length
Why is it not practical for a mag to be 22.5 times in magnification
A normal print letter is about 2mm wide. If this was magnified by 22.5 times this would be 45mm or 4.5 cm wide which is wider than msot objective lenses so the user wont even be able to view one whole letter at a a time.
Why dont we make telescopes with low powers of 1 objective and 5 for eyepiece as we would get mag of 5 dioptres. Why dont lva telescopes use such low power lens
Focal length is 1m
Focal length of eyepiece is 1/5= 0.2m -> fe’= -0.2
Distance= fo’-fe so 1- -0.2= 1.2m
Clearly not feasible for use as lva, too long
When are two cylindrical lenses obliquely crossed
What can any pair of obliquely crossed cylinders be replaced by
Two cylindrical lenses are obliquely crossed if their axes are not parallel or mutually perpendicular.
Any pair of obliquely crossed cylinders can be replaced by an equivalent sphere-cylindrical combination.
When two cylinders are combined with axes obliquely crossed there is a induced spherical component S and a cylindrical one C
When can you get obliquely crossed cylinders
if you get your refractive correction incorrect
if the axis of the cyl is wrong when you refract you induce obliquely crossed cylinders.
So resultant cylinders from incorrect refractive correction.
If an eye needs a a cylinder correction of -1.00DC x 20 and is incorrectly given a correction of -0.50DC x 130
Resultant residual error with a spherical and cylindrical component.
Since the eye needs a correction of -1.00DC x 20 the eye itself must have a cylinder of +1.00DC x 20. Resultant combination is worked out from the +1.00
So the resultant sphere cylindrical error is the combination of the eyes cylinder and the incorrect -0.50 x 130 cylinder given.
Why is it important to calculate the correct cyl to
To put on the front of a bi toric hard cl to give the correct rx