Visual Optics Exam 2

When does refractive error occur?

when there is a mismatch between the refractive power of the eye and its axial length

When does myopia occur?

when an eye has too much positive power for the axial length or too long an axial length for the refractive power

When does hyperopia occur?

when an eye has too little positive power for the axial length or too short an axial length for the refractive power

Where is the far point in emmetropia?

far point is infinity so the eye needs zero vergence at the principal plane in order to forma clear retinal image

Where is the far point in myopia?

far point is a real object location, so the eye needs negative vergence at the principal plan to form a clear retinal image

Where is the far point in hyperopia?

far point is a virtual object location behind the eye so the eye needs positive vergence at the principal plane to form a clear retinal image

What is the K value for an emmetrope?

K = 0 since K' = F

What does the secondary focal point of the correcting lens must coincide with in refracting an ametropic eye to produce a clear retinal image of a distant object?

must coincide with the far point

Where does a correcting lens form an image for a distant object?

at its secondary focal point - correcting lens creates incident vergence at the eye's principal plane that results in a clear retinal image after refraction by the eye

When does axial ametropia occur?

-when an eye has an inappropriate axial length while its refractive power is "normal"

-in a reduced eye model, the power of an axial ametrope is +60 D while the axial length is some value other than 22.22 mm

When does refractive ametropia occur?

-when an eye has an inappropriate refractive power for its "normal" axial length

-in the reduced eye model, the axial length of a refractive ametrope is 22.22 mm while the refractive power is some value other than +60 D

What are the F and k' values for axial ametropia for myopia and hyperopia?

both: F = +60 D

-myopia: k' > 22.22 mm

-hyperopia: k' < 22.22 mm

What are the F and k' values for refractive ametropia for myopia and hyperopia?

both: k' = 22.22 mm

-myopia: F > +60 D

-hyperopia: F < +60 D

What would an image look like if the reduced eye views an object that is not conjugate with the retina?

image of the object will be out of focus - blur circle

What does the size of a blur circle depend on?

depends on the pupil diameter

Blur Circle Diameter Formula

j = g[(K - L)/K']

j = blur circle diameter

g = pupil diameter

K = the eye's ocular correction (vergence needed at principal plane to get an image on retina without accommodation)

K' = image vergence needed leaving the eye's principal plane to get an image on retina

L = object vergence at the eye's principal plane; for an object at infinity L = 0

How big is the blur circle if the pupil is smaller?

the smaller the pupil, the smaller the blur circle - PINHOLE

Rayleigh Criterion

objects can be resolved if their blur circles were separated by j/2

Depth of Focus

-dioptric range that appears clear in the image when taking a picture with a large aperture - the corresponding object range is known as the depth of field

-measure of tolerance of the eye to blur

What is the relation between depth of focus and aperture size?

depth of focus decreases as the aperture size increases

Hyperfocal Distance

-when an eye or optical system is focused at the hyperfocal distance, point Qd is at infinity

-to solve, take the reciprocal of E and make it a negative distance (-1/E)

What does the depth of focus depend on?

pupil diameter

Depth of Focus Formula

l'p - l'd = 2(j/g)k'

j = blur circle diameter of 0.010 mm

g = pupil diameter in mm

k' = axial length in mm

Anisometropia

condition when patients have unequal refractive errors in the two eyes

What can unequal retinal image sizes (aniseikonia) lead to?

-headaches

-asthenopia

-photophobia

-reading difficulty

-anomalous space perception

How can retinal image size in the reduced eye model be estimated by the angular magnification of the chief ray?

-the chief ray enters the eye through the center of the entrance pupil (at P); in the reduced eye model, the entrance pupil is taken to be located at the principal plane, which is also the front surface of the reduced eye - thus the chief ray enters the reduced eye through principal point P

-the chief ray is important in determining the size of the retinal image, whether the retinal image is in focus or blurred

What happens to the chief ray in a reduced eye if the retinal image is in focus?

the location where the chief ray intersects the retina determines the height of the image

What happens to the chief ray in a reduced eye if the retinal image is blurred?

-the chief ray from any given object will intersect the retina at the center of the blur circle in the image of that point

-the location of the chief ray can be used to define the height of the blurred retinal image (the actual size of the blurred image will extend beyond the chief ray location)

What angle does the incident chief ray subtend?

-angle of u(o) at the principal plane

-subscript "o" on the incident angle signifies that it is the angle subtended by the object

-the chief ray bends after refraction at the principal plane according to Snell's law

-the refracted ray makes an angle of u' with the optic axis

What is the ratio u'/u(o) when the angles are in radians?

-0.75, since u'/u(o) = n/n', and n = 1 and n' = 4/3

-for a distant object the optical image is formed at the secondary focal point of the eye which is a distance of f'e from the principal plane

What is the retinal image size in the emmetropic reduced eye?

-for the emmetrope, the image h' is a focused image on the retina so the distance f'e is also the axial length, k'

-assuming small angles, tan u' = u' = -h'/f'e, so the retinal image size is given by: h' = -0.75u(o)f'e = -0.75u(o)k', with angle u(o) in radians and f'e equal to the secondary focal length of the eye (22.22 mm)

What are the two images in the uncorrected ametropic eye?

-optical image

-retinal image

Optical Image (h')

-formed either in front of the retina for a myope or behind the retina for a hyperope (the retina actually blocks formation of the optical image for the hyperope but the light converges toward that image)

-for a distant object it is located at a distance of f'e from the principal plane

Retinal Image (h'b)

-a blurred image located on the retina at a distance k', the axial length, from the principal plane

-the size of this image is used to determine the spectacle magnification

What is the ratio of the refracted and incident angles for the chief ray in an ametropic reduced eye?

0.75, because the ametropic reduced eye has the same index of refraction as the emmetrope

How is the retinal image size (h'b) determined?

by the chief ray location at the retina:

tan u' = u' = -h'b/k' so h'b = -0.75u(o)k'

What does the size of the blur circle (j) depend on?

depends on the pupil size (g)

What is the size of the blurred retinal image in the uncorrected axial ametrope dependent on?

depends on the axial length, with axial myopes having a larger image than the emmetrope and axial hyperopes having a smaller image than the emmetrope

What is the size of the retinal image in the uncorrected refractive ametrope?

the same as the retinal image size in the emmetrope, this is because the axial length k' is also 22.22 mm in the refractive ametrope, and the size of h'b is determined by the chief ray location

When does the retinal image size change, and why?

when a correcting spectacle lens is worn - this happens because the spectacle lens bends light and changes the angle at which the chief ray enters the eye (compared to the uncorrected case)

Spectacle Magnification Formula

SM = retinal image size in the corrected ametropic eye/retinal image size in the uncorrected ametropic eye

SM = h'2/h'b = u/u(o) = f'sp/k = K/Fsp

u = angular subtense of the image formed by the lens (h'1)

u(o) = angular subtense of the distant object viewed without the lens

(u and u(o) are subtended at the eye's entrance pupil)

What is the spectacle magnification for hyperopes, and why?

SM is greater than 1 because u is a steeper angle than u(o) and the secondary focal length of the correcting lens is longer than the far point distance

What is the spectacle magnification for myopes, and why?

SM is less than 1 because u is a shallower angle than u(o) and the secondary focal length of the correcting lens is shorter than the far point distance

What is the spectacle magnification given by when the spectacle prescription is considered a thin lens?

SM = 1/(1-dFsp)

d = vertex distance

Fsp = power of spectacles

Relative Spectacle Magnification (RSM)

compares the size of the retinal image in a corrected ametrope to that in an emmetrope:

RSM = retinal image size in the corrected ametrope/retinal image size in the emmetropic eye = h'2/h'

RSM = power of emmetropic eye/power of the ametropic eye-correcting lens system

RSM = F emmetropic eye/(Feye + Fsp - (d)(Feye)(Fsp))

Feye = power of the ametropic eye

Fsp = power of correcting lens

d = distnace from the second principal plane of the correcting lens to the first principal plane of the eye

When is the retinal image size independent of axial length?

-when the spectacle vertex distance "d" is equal to the primary focal length of the eye

-this happens because the ray through the primary focal point travels parallel to the optic axis after refraction by the eye

-in this case, the retinal image for the corrected axial ametrope is the same as that for the emmetrope so RSM is 1

Knapp's Rule

a clinical principal that advises you to minimize the difference in the corrected retinal image sizes of an anisometropic patient in the following ways:

-correct axial anisometropia with spectacles

-correct refractive anisometropia with contact lenses

Where should the spectacle lens be placed for spectacle correction of axial anisometropia?

at the primary focal plane of the eye, at Fe - this should minimize differences in retinal image size

Why should contacts be avoided for axial anisometropia?

contacts preserve the differences in retinal image size across refractive errors because the retinal image size with a contact lens only depends on the axial length

How is the retinal image size in corrected refractive ametropia determined?

-since the axial length of the refractive ametrope is the same as that in the emmetrope, it is solely determined by the spectacle magnification (SM)

-since SM is minimized with a contact lens (SM = 1) then refractive anisometropes should be corrected with contact lenses

Aniseikonia

-occurs when there is a noticeable difference in perceived retinal image sizes between the two eyes

-if one assumes that the perceived retinal image size is determined solely by the size of the retinal image, then the ratio of the RSM values for each eye can be used to estimate the amount of aniseikonia

OD retinal image size/OS retinal image size = RSM(OD)/RSM(OS)

Where is the primary or anterior focal point of the eye (Fe) located for axial ametropia corrected by spectacles at Fe?

located at -1/+60 D or -16.67 mm in front of the eye

What is the size of the retinal image when the spectacle plan is at Fe?

retinal images are the same size for any axial length

What is the SM for myopes with spectacle correction in axial ametropia?

SM < 1

What is the SM for hyperopes with spectacle correction in axial ametropia?

SM > 1

What is the RSM for myopes and hyperopes with spectacle correction in axial ametropia?

RSM = 1

What is the SM for myopes and hyperopes with contact lens correction in axial ametropia?

SM = 1

What is the RSM for myopes with contact lens correction in axial ametropia?

RSM > 1

What is the RSM for hyperopes with contact lens correction in axial ametropia?

RSM < 1

What is the SM for myopes with spectacle correction in refractive ametropia?

SM < 1

What is the SM for hyperopes with spectacle correction in refractive ametropia?

SM > 1

What is the RSM for myopes and hyperopes with spectacle correction in refractive ametropia?

RSM = SM, no axial length effect

What is the SM for myopes and hyperopes with contact lens correction in refractive ametropia?

SM = RSM = 1

What is the uncorrected retinal image size (h'b) in myopic axial ametropia compared to the emmetropic eye?

larger than emmetropic eye due to increased axial length (about 1.5% per diopter of myopia)

What is the uncorrected retinal image size (h'b) in hyperopic axial ametropia compared to the emmetropic eye?

smaller than emmetropic eye due to decreased axial length (about 1.5% per diopter of hyperopia)

What is the uncorrected retinal image size (h'b) in both myopic and hyperopic refractive ametropia compared to the emmetropic eye?

have the same retinal image size as in emmetropia because the axial length is the same as that in the emmetropic eye (k' = 22.22 mm)

What two factors determine corrected retinal image size?

-spectacle magnification

-axial length

What results in spectacle magnification?

-smaller retinal image with a minus correction (myopia)

-smaller retinal image with a plus correction (hyperopia)

-magnification (or minification) is approx. 1.5% per diopter of spectacle lens power

What does spectacle magnification depend on?

-spectacle lens power (Fsp) and vertex distance (d)

-as vertex distance decreases to zero (contact lens), spectacle magnification goes to 1 and thus corrected and uncorrected image sizes are equal for contact lens correction

What does axial length determine in regards to corrected retinal image size?

the uncorrected image size (h'b)

What is corrected retinal image size in axial ametropia like?

-spectacle magnification and axial length are opposing factors that tend to cancel each other

-myopia: minification due to the spectacle lens tends to cancel out the magnification due to the increased axial length

-hyperopia: the magnification due to the spectacle lens tends to cancel out the minification due to the decreased axial length

What is the axial length like in corrected retinal image size in refractive ametropia?

axial length is constant (same as emmetrope) so spectacle magnification acts alone in determining the corrected retinal image size

What is axial ametropia like with spectacles?

-spectacle magnification cancels the effect of axial length

-axial myopes and hyperopes corrected with spectacles would have corrected retinal image sizes that match the emmetropic retinal image size

What is axial ametropia like with contact lenses?

-no spectacle magnification, so corrected retinal image size is determined by axial length

-an axial myope corrected with contact lenses would have a larger retinal image size than the emmetrope

-an axial hyperope corrected with contact lenses would have a smaller retinal image size than the emmetrope

What is refractive ametropia like with spectacles?

-spectacle magnification determines the corrected retinal image size since axial length is the same for refractive ametropes and emmetropes

-a refractive myope corrected with spectacle lenses would have a smaller retinal image size than the emmetrope

-a refractive hyperope corrected with spectacle lenses would have a larger retinal image size than the emmetrope

What is refractive ametropia like with contact lenses?

-no spectacle magnification so corrected retinal image size is determined by axial length

-refractive myopes and hyperopes corrected with contact lenses would have corrected retinal image sizes that match the emmetropic retinal image size

What are the uncorrected, spectacles, and contact lenses retinal image sizes in axial myopia compared to emmetropia?

-uncorrected: larger

-spectacles: same

-contact lenses: larger

What are the uncorrected, spectacles, and contact lenses retinal image sizes in axial hyperopia compared to emmetropia?

-uncorrected: smaller

-spectacles: same

-contact lenses: smaller

What are the uncorrected, spectacles, and contact lenses retinal image sizes in refractive myopia compared to emmetropia?

-uncorrected: same

-spectacles: smaller

-contact lenses: same

What are the uncorrected, spectacles, and contact lenses retinal image sizes in refractive hyperopia compared to emmetropia?

-uncorrected: same

-spectacles: larger

-contact lenses: same

What is retinal stretching and visual acuity like in myopia?

-retinal image is larger in axial myopia but foveal cones are likely to be more widely spaced

-these two factors tend to balance each other, so that conventional angular measures of acuity are often normal in myopia

What is visual acuity like in myopia?

-acuity is significantly reduced in myopia when you compensate for the larger retinal image in myopic eyes

-myopes have normal acuity when it is expressed in angular units such as cycles/degree; however, acuity is reduced compared to emmetropes when acuity is expressed in retinal units of cycles/mm

-this result implies that neural stretching in axial myopia reduces acuity

What is the ciliary muscle like in the unaccommodated state?

ciliary muscle is relaxed and the lens is in a flattened shape

What is the ciliary muscle like during accommodation?

-ciliary muscle contracts, the lens zonules relax and the lens capsule contracts

-the lens assumes a more spherical shape with the anterior portion bulging forward

How does the radius of curvature of the lens change during accommodation?

-radius of curvature of the anterior and posterior lens surfaces are shorter (steeper curvature) than in the unaccommodated state; this reduction in the radii of curvature gives the lens more positive power

-the anterior surface of the lens steepens by a greater amount than the posterior surface

How does the radius of curvature of the lens nucleus change with accommodation?

-the total increase in dioptric power of the lens with accommodation is not due entirely to the changes in the surfaces of the lens cortex

-the effective radii of curvature of the lens nucleus also decreases with accommodation

How does the equatorial diameter of the lens change with accommodation?

as the lens zonules relax, the lens diameter becomes smaller in the vertical plane (i.e. the lens aperture decreases)

How does the center thickness of the lens change with accommodation?

the increase in thickness in the horizontal plane during accommodation is primarily due to the anterior surface bulging forward

How does the location of the optic axis of the lens change with accommodation?

the forward movement of the anterior lens surface results in an effective movement of the lens toward the cornea, thus the anterior chamber depth decreases during accommodation

How does the vertical position of the lens change with accommodation?

if the relaxation of the zonules is sufficient, there is a slight vertical drop in the lens position due to gravity

How does the refractive power and focal length of the eye change with accommodation?

-the effective forward movement of the lens and its steeper shaped surfaces result in more positive refractive power of the eye, thus the primary and secondary focal lengths of the eye decrease

-compared to the unaccommodated state, the principal planes move backwards and the nodal points move forward in the accommodated eye

What is the vergence stimulus like to accommodation?

-when the vergence at the principal plane is equal to the far point vergence (K) there is no vergence stimulus to accommodate

-this is based on the definition of the far point - that object location that produces a clear retinal image in the uncorrected, unaccommodated eye

-there is a stimulus to accommodate when the vergence incident at the principal plane becomes more negative or less positive than the far point vergence

-as an object is moved closer to the eye, the vergence incident at the principal plane becomes more negative (for real objects) or less positive (for virtual objects, as for a corrected hyperope)

What is the accommodative demand at the principal plane defined as?

ocular accommodation

What is the accommodative demand at the spectacle plane defined as?

spectacle accommodation

Ocular Accommodation Formula

A = K - L

A = ocular accommodation

K = vergence incident at eye's principal plane for an object at the far point (ocular correction in diopters, negative for myopia and positive for hyperopia)

L = object vergence at principal plane of the eye

A should always be positive, since it represents the increase in the eye's power during accommodation

Spectacle Accommodation Formula

Asp = -Lsp

Asp = spectacle accommodation

Lsp = object vergence at spectacle lens

Asp should always be positive, since it represents the increase in the eye's power during accommodation

True Near Point of Accommodation

-the object location that results in a clear retinal image when the uncorrected eye is fully accommodated

-this is analogous to the far point for the unaccommodated eye

Ocular Amplitude

the dioptric power change within the eye obtained with maximal accommodation, measured at the principal plane

Ocular Amplitude of Accommodation Formula

Amp = K - B

K = the vergence incident at the eye's principal plane when the object is at PR in the uncorrected case, or when a spectacle lens forms an image at PR

B = vergence incident at eye's principal plane when the object is at PP (true near point) in the uncorrected case, or when a spectacle lens forms an image at PP

Measured Near Point (MNP)

-the object location that results in a clear retinal image when the corrected eye is fully accommodated

-with the object at the measured near point, a spectacle lens forms an image at the true near point (PP)