7: astigmatism .

what is astigmatism

a condition of a refraction in which the image of a point objects is not a signle point, but two focal lines at different distances from the optical system

the 2 focal lines are perpendicular to eachother

causes of astigmatism: toroidal surfaces 

rugby balled shape: has maxiumum curvature in one and minimum in another at right angles to eachother 

radius of curvature has a meridian of max curvature and other has minimum curvature

if an eye has a toroidal refractive surface eg cornea or les then the power of the eye will not be the same in all meridians

how do we measure the curvature of the front surface of cornea

done using a keratometer 

the keratometry reveals that the cornea is truly sphercal even in the central cornea near optical axis

front surface of cornea is steepest( shortest radii) in vertical meridian

shorter radius of curvature = more myopic

more causes of astig

cyrstalline lens 

either or both of its surfaces may be toroidal

even if corneal and crystalline lens surfaces are spherical, decentration or tilting of the crystlline lenses with respect to the cornea will give rise to astigmatism

what is lenticular astigmatism

astigmatism that is caused by the lens corneal astig caused by cornea

how is astigmatism corrected 

sph/cyl lenses are used to correct astigmatsm by equalising the difference in power between the principal meridians of the eyes 

e.g if the vertical meridian of the eye is 2.00D more powerful than the horizontal : -2.00 × 180 will correct it

oblique astigmatism - first meaning 

if light from a point object passes obliquely through a spherical surface or lens then it will not form a point image

different object distance when off axis so image is different distance

point object is well below the principal axis, it gives rise to the same imagery we get in astigmatism that is caused by toroidal surface   

image of a point object in an astigmatic eye 

incoming rays of light are parallel 

a vertical focal line is formed in front of the retina and a horizontal one is just next (infront) to the retina

vertical meridian (bue) forms a horizontal line focus (blue)

meridian formes focal lines at right angles

horizontal meridian in red forms the vertical line focus in red

both line foci formed in front of retina but one line is much closer

how do we end up with line images when we start with a point object

between the 2 focal lines of a toroidal lens: halfway between is a blur circle  

rays of light diverge from point object B and are refracted by a toroidal surface/ gives rise to astagmatic images 

forming a point image 

covered over the lens besides the transparent section through which light can travel through 

if light travels through the horizontal section a point image is created 

if horizontal gap ov opaque cover is moved down, what happens to focal line

light only travels through portion of lens 

point image moves up 

if gap is placed at the top where is the focal point

focal point forms at the bottom part

light coming throgh different portions of the lens is imaged in different places

point images join to form line focus

horizontal meridian of the lens is giving rise to point images which when joined together form a vertical line image

whats the interval of sturn

measurement of the distance between the 2 focal lines 

what produces the horizontal focal point

if you place a lens where portion viewed is a vertical stip , it forms a focal point on the horizontal focal line 

vertical meridian of the lens is giving rise to a point images which when joined together form a horizontal line image

when vertical slither is moved to the left :

what does the eye see

depends what falls on the retina

if vertical line is in front then the image formed on the retina is mostly influenced by the horizontal focal line 

the horizontal focal line corresponds to blur that makes horizontal detail sharper and vertical blurrier 

so person sees the vertical lines blurred, horizontal clear 

what is seen if the retina is closer to the vertical focal line?

vertical focal line is in front of the retina

produces horizontal blur on the retina 

so vertical images look blurred, horizontal appear clear

what is seen if the reitna is closer to the horizontal focal line

horizontal line is in front of the retina 

produces vertical blur on the retina

therefore horizontal objects appear blurred

vertical lines look clearer

what is see when retina is located ON the vertical/horizontal lines

if retina located at X: vertical lines will be seen clearly 

if located at Y: horizontal lines will be seen clearly ( V lines hugely out of focus)

if retina is located at Z then all orientations will be equally blurred 

spherical vs astigmatic defocus 

top right shows spherical blur: not astig as blurred in all directions 

C:  : astigmatism shows horizontal lines are blurred , vertical clearer

means that the vertical meridian of the eye is too flat so light travelling along vertical focuses differently from light travelling along vertical 

D: astigmatism, horizontal is more clear than vertical

astigmatic defocus when the cyl axis is not H or V 

C&D same as last photo

E and F show oblique astigmatism: prinicpal meridians are not at 90 or 180

E: plano/ -1.00 × 45

F: plano/ -1.00 × 45

cyl axis at 45 or close to 45, or 135 or close to 135  shows most oblique 

threshold reached during VA measurement: difference in spherical ametropia and astig 

in spherical, since all lines are blurred, many can only read up to a certain line 

with astig, some letters on lowest line can be read, spherical cannot proceed further beyond a certain line

orientation in the same place as lines of alphabet

what is the with rule of astig 

the steepest meridian of the cornea is vertical 90 degrees or at least near

vertical meridian focuses light sharply ,

blur vertical lines more, horizontal less

what is the against rule of astigmatism

the steepest meridian of the cornea is the horizontal one

horizontal meridian focuses light sharply so horizontal lines more blurry

oblique astigmatism

the principal meridians are not near 90 or 180   

horizontal / vertical and oblique on letter chart 

bottom left: against the rule of astig as axis is at 90 or near 90. 180 line is blurred

bottom middle: with the rule as axis is at 180. +2.00 added to simulate a -2.00

why might it be easier to read letters with astig and not spherical blur

some letters have vertical elements: P, D, H, N, T

some have horizontal : H L, T , A

impact of astigmatism on distance vision 

uncorrected astig reduces distance vision 

hyperoppes rely on accomodation to see clearly, so even mild astigmatism can interfere with near and distance vision 

myopes less affected by astig as naturally focus for near tasks

what is irregular astig 

cornea is distored- cone shaped; 

principal meridians are not at right angles to eachother

if cause of irregular is corneal, a contact lens can provide much better correction than spectacle lens

what is compound myopic astigmatism

both focal lines are in front of the retina 

eg -2.00/-2.00 × 180

along 180 eye is myopic by -2.00D

along 90 the eye is myopic by -4.00D

simple myopic astigmatism

one focal line on the retina, other focal line in front

eg 

plano/ -4.00 × 180 

along 180 is emmetropic, along 90 is myopic by -4.00D 

compound hyperopic astigmatism

both focal lines behind the retina

eg +2.00/+2.00 × 90 

simple hyperopic astigmatism

one focal line on the retina, other focal line behind

+4.00/-4.00 × 180 

along 180 : hyperoopic by +4.00 , along 90: emmetropic 

mixed astigmatism

one focal line behind the retina, the other line in front

+2.00/-4.00 × 180

along 180: hyperopic by +2.00D 

along 90: myopic by -2.00D

with and against rule 

more curvature means a shorter/smaller radius of curvature

with: steepest vertical 

against: steepest horizontal

what is with rule astig corrected with

corrected with -ve with an axis of 180 or near 180

or corrected with a +ve with axis of 90 or near 90

hyperopia in an eye means eye or meridian is under powered 

since 90 meridian is less hyperopic, its less underpowered than 180 meridian, hence this eye has WTR

-3.00/+1.25 × 80 : Why is this with the rule?

eye is myopic by -3.00D along 80 meridian and myopic by -1.25  along 170

the 80 is more myopic so more powerful than the 170

against rule astig corrected with?

corrected with - ve cyls with axis of 90 or near 90

or with +ve cyls with axis 180 or near 180 

+2.00/-1.00 × 90 

eye is hyperopic by +2.00D along 90 meridian and hyperopic by +1.00D along 180

since the 180 meridian is less hyperopic , its less underpowered than 90 meridian 

so this has ATR

+1.00/+1.25 × 10 : why is this against 

eye is hyperopic by +1.00D along 10, and hyperopic by +2.25D along 100

since the 10 meridian is less hyperopic its less underpowered than 100 meridian ( more powerful than 100)

so this eye is against the rule

oblique astigmatism (2nd meaning)

ocular astig in which the two principal meridians are neither approx horizontal nor vertical

corrected with cyls with axis 45 or 135 or near

doesnt matter if cyl power is + or -

-1.50 /-1.00 × 45 : why is this oblique 

the eye is myopic by -1.50D along 45 meridian , and myopic by -2.50D alog 135

since principal meridian are not V and H and not near this eye has oblique astig

Accomodation and astigmatism

Accom shifts the interval of sturn left towards the cornea so the eye may be able to moce the blurred circle onto the retina or to accomodation to place one or both focal lines on the retina

uncorrected hyperopic eyes with astig accomodate so that the blurred circle is on retina and vertical focal line is on/near retina

doesnt apply to myopia

how astig is corrected with sph/cyl lenses:

plano/ -2/00 × 180

H meridian is emmetropic: forms its focal line V on the retina

V meridian myopic: forms its focal line H, in front of the reitna 

V has 2D more positive power than the H meridian  

if plano /-1.00 × 180 is added, -1.00D is added to the V meridian 

so half astig is corrected 

V line stays where it is as nothing is added to the V , H line moves closer yo retina: both focal lines get shorter as interval is reduced 

astigmatic fan chart 

if the lines are clear and equally clear theresno astigmatism 

if some blurred and some not then astug