MagnificationMagnificationAmy Nau, O.D.

http://www.purdue.edu/hr/images/magnifyingGlass.jpg

Types of MagnificationTypes of Magnification

AngularApparent

(Conventional/ Effective/Loupe)

Axial/longitudinalCombined/totalCorticalRelative distance

Electronic/transverseIso-accommodativeLateral/linearSpectacleRelative spectacleRelative sizeShapePower

Angular MagnificationAngular Magnification

Ratio of object angle to image angleThis is why objects appear larger as they move

closer to the eye

Angular Magnification

The object is not changed in position or size, but has a lens between the object and the eye which makes it appear larger (magnifying glass, hand magnifier, telescopes)http://www.medrounds.org/optics-review/uploaded_images/Figure34-745600.jpg

M = tan α′/tan α M=angle image device /angle original object

Angular MagnificationAngular Magnificationbasic conceptsbasic concepts

Mag 0-1 means image is smaller than objectMag >1 means image is larger than objectMag=1 same size (no mag)If the image is farther from the lens than the

object it will be larger (magnified) and vice versaImage is erect if on same side of lens as object

(like a mirror)- virtual image+ upright/ - inverted

Linear/Transverse Magnification

Ratio of image vergence to object vergence L’/LRatio of image size to object size= I/O

http://www.medrounds.org/optics-review/2006/05/27.html

Problem image size/object size or image Problem image size/object size or image dist/obj distdist/obj dist

Calculate transverse mag for the followingF=+8Object distance 100 cm image distance is 1/8=0.14m

So, 0.14/1=0.14 (minimized)

Axial (Longitudinal) MagnificationAxial (Longitudinal) Magnification

M= M1X M2Axial magnification is used when talking about

3D objectsAxial magnification is the distance between the

two image planes divided by the distance between the two object planes (extreme anterior and posterior points on the object with their conjugate image points)

Axial (Longitudinal) MagnificationAxial (Longitudinal) Magnification

Take incoming vergence front and back of object and calculate the emergent vergence front and back then get the ratio.

Apparent MagnificationApparent Magnification

Syn: Conventional/Effective/Loupe/RelativeM e = dFWhere d = distance in meters to the object (image is

formed at infinity)

Question: A +24.00D lens is used as a hand held magnifier with the patient viewing an object that is 50cm from the eye and at the focal point of the lens. How much larger do things appear to the patient?

Answer: d = 0.50m, F= +24.00D, M e = dF = 0.50(24) = 12X

This indicates that closer working distances result in less effective magnification.

Conventional MagnificationConventional Magnification

Conventional Magnification = Mc = dF + 1 The underlying assumption in this equation is

that the patient is “supplying” one unit (1X) of magnification otherwise it is the same as apparent magnification

Used for low vision

Total (Combined) MagnificationTotal (Combined) Magnification

Generally used for microscopes, but basically you multiply the individual lens mags together

MT= M1 X M2 X M3…..So you have a 15 x eyepiece and a 10x

objective for total mag of 150x.

Electronic MagnificationElectronic Magnification

CCTV, computers, video, BrainportIt is equal to the ratio of the size of the image on

the screen to the size of the original object being viewed.

Example: an object 2cm in height measures 6 cm on the screen, the magnification is 6/2 = 3 . ✕

relative distance magnificationrelative distance magnification

The magnification that results from decreasing the distance between an object and the eye. It is expressed as

Md = x/x′where x and x′ are the initial distance and the new

distance, respectively.

Example: if the viewing distance is decreased from 60 cm to 20 cm, Md = 60/20 = 3 . ✕

Iso- Accommodative MagnificationIso- Accommodative Magnification

The magnification of a lens (or lens system) when the distance of the image from the eye (or spectacle plane) formed by a magnifier is equal to the distance of the object from the eye viewed without the magnifier. Thus the same amount of accommodation (or near addition) is required with or without the magnifier. It is equal to

M = 1 + (F/D)where F is the power of the magnifier (assumed to

be so close to the eye as to ignore the distance separating them) and D the object vergence.

Spectacle MagnficationSpectacle Magnfication

How much glasses magnify or minify the retinal image size

It is >1 in the hyperopic eye, <1 in myopia. With a contact lens, this magnification is 1 whatever

the refractive error.

Depends on Lens thicknessMaterial (index)Vertex distanceBase curve of the front of the lens

Spectacle MagnificationSpectacle Magnification

SM=(shape factor) x (power factor)Shape factor relates to base curve and lens

thicknessPower factor relates to overall lens power and

vertex distance

SM = (1/1-(t/n)D1) x (1/1-hD)◦Where: n=index of refraction; D1=front surface power

(base curve); D = total lens power; h= vertex dist +3mm (b/c calculated at entrance pupil not corneal plane)

Spectacle MagnificationSpectacle Magnification

In the case of aniseikonia, eikonic lenses can be prescribed which try to reduce magnification effects by manipulating◦BC◦Thickness◦Vertex distance

◦Can be cosmetically unacceptable

What is the SM for each lens, the difference in mag percent and how can you minimize the difference?

OD: +1.50; BC +6.25; t=3mm OS: +4.50; BC +9.25; t=5mm Vertex 12mm N=1.498

SM OD = (1/1-(0.003/1.498)(6.25)) (1/1-(0.015)(1.50)=1.036 %SM= (SM-1)(100)= 3.6% SM OS: (1/1-(0.005/1.498)(9.25)) (1/1-0.015)(4.50)=1.107 % SM = 10.7%

Difference in SM is thus 7.1% You can try to manipulate BC, t, vertex, index. Need to check each

one to see which may work

Spectacle MagnificationSpectacle Magnification

Rare to change all 3 variablesChoose small, round frame fitting close to faceAspheric lensesAcceptability of poor cosmesis usually related to

functional outcome.

Relative Spectacle MagnificationRelative Spectacle Magnification

The ratio of the retinal image size in the corrected ametropic eye to that in a standard emmetropic eye.

Relative Size MagnficationRelative Size Magnfication

The magnification which results from increasing the actual size of an object viewed. Examples: a larger TV screen; a larger print book than one used previously. It is expressed as

Ms = h2/h1where h2 and h1 are the sizes of the enlarged

object and the initial object, respectively.

Syn. size magnification; relative size enlargement.

Lateral MagnificationLateral Magnification

Magnification of a lens or of an optical system, expressed as the ratio of the size of the image h′ to the size of the object h. It is usually denoted by

M = h′/h = l′/l = L/L′where l′ and l are the distances of the image

and object, respectively from the principal plane of the lens (or lens system) and L and L′ the object and image vergences

Cortical Magnification

Term referring to the fact that the amount of cortical area devoted to processing visual information from the central area of the retina far exceeds the amount devoted to the peripheral retina. It is estimated that about 25% of the cells in the visual cortex are devoted to processing the central 2.5º of the visual field.

http://webvision.med.utah.edu/imageswv/fovea-periphery.jpg