7.3 the astigmatic image Flashcards
What happens when observing an object point at presence of astigmatism?
line foci are formed
What are one of the paradox of astigmatism?
the lines are perpendicular to the meridian aghast is at focus
What does astigmatism mean?
not stigmatic-
What does stigmatic mean?
means point to point imagery that means a single point object is imaged as single point image which is not the case in astigmatic images
What do the line foci represent?
represents extremes of shapes that can be formed in a astigmatic image
How do you and what happens when viewing an astigmatic image?
putting magnifier glass over
-get progression of blurring between the 2 extremes the horizontal line focus and vertical line focus
What happens as you move away from the horizontal line focus ?
get horizontal blur elipse
line limiting form of elipse
-the more ways you get a circular patch -disc of least confusion
-even more away the ellipse becomes vertical before it becomes the vertical line of focus
-progression of shapes of blur as we move through focus in a astigmatic image
-circles and lines are special form of elipse.
What is the disc of least confusion (DLC)?
-circular blur patch located dioptrically midway between the astigmatic foci
What is the best approximation to point object?
circular blur- all diagrams show single point of light
What is the best approximation to point object called ?
-circle of least confusion- point in between 2 line foci
What is Best vision sphere (BVS)?
-It is the spherical correction in the spectacle plane that places the disc of least confusion on the retina for distance vision.
What are the definitions for analysis?
Take θ to be the least powerful meridian with power Fe θ ; this will be the sphere component when the prescription is written in negative cyl form
-always at right angles to each other
What is the most powerful meridian ?
θ + 90 degrees is the more powerful Meridan with power Fe theta + 90
What is the least powerful meridian ?
Take θ meridian as least powerful meridian with power Fe θ
What is the expression of the length of the astigmatic line for the least powerful meridian?
From similar triangles: a=p(l’θ-l’θ+90/l’θ)=p(L’θ+90-L’θ/L’θ+90)
How does the pupil size and astigmatic line correlate?
the bigger the pupil size the longer the astigmatic line
What is the expression of the length of the astigmatic line for the most powerful meridian?
b=p(l’θ+90-l’θ/l’θ+90)=p(L’θ-L’θ+90/L’θ)
What is the length of focal line expression for a distance object?
L’θ=Feθ
What is astigmatism defined as ?
the difference in power between the principal meridians
What is the Ast equation?
Ast= Fe θ+90 - Feθ
What are the expression when distant object- in the θ+90 meridian?
a= p(-Ast/Feθ+90)
What are the expression when distant object- in the θ meridian?
b= p(-Ast/Feθ)
What are the dimensions of the elliptical blur?
- working at general distance (retina can be at any point) - l’z
- The method used to find the length of the astigmatic lines can be used to find the major and minor axes of the elliptical blurs
What is l’z?
the general distance
What is l’θ?
focus distance of the least powerful meridian - which can be used to determine size of blur elipse
What are the dimension of the elliptical blur equation for major ?
x= p(L’z-L’θ/L’z)
What can the major and minor do?
Can flip around depending on relative magnitudes
What are the dimension of the elliptical blur equation for minor?
y=p(L’θ+90-L’z/L’z)
What is the dioptric location of DLC (L’z)
The DLC occurs when major and minor axes of the elliptical blur are equal
What is the dioptric location of DLC (L’z) equation?
p=(L’Z-L’θ/L’z)=p(L’θ+90-L’z/L’z)
What is the DLC for a distant object equation?
L’θ= Feθ
L’θ+90=Feθ+90
THEREFORE
L’z= (Fe θ+90 + Fe θ / 2)- shows dioptrically midway
What do we do to find location of DLC?
L’z equation
How do we find size of DLC?
knowing the location, we can substitute into either expression for the major or minor axis of the ellipse to find the diameter of the DLC
-IF PUPIL size is higher,, blur is larger , then the DLC will be larger and astigmatism is higher
What is the equation for the size of the DLC?
z= (p x Ast / Fe θ+90 + Feθ)
Take an eye with compound myope astigmatism
-0.50DS/-2.00DC X135
Astigmatic blur
- This could be produced by an eye with
Fe135 = 60.5 D
Fe, 45= 62.5D
K’ = 60D
Means main blur is along the 45 meridian
and the along 135 is the less blur
-Blurr elipse from examiners view
How to calculate the major and minor axes of the blur elipse ?
E.g (p=4mm)
Draw table - have in notes
-Blurr elipse from examiners view
How to predict the appearance of astigmatic image?
superimpose blurs on lines to predict blurred image
- can treat any object as a collection of points and each of those points become a blur ellipse
- Have series of lines (horizontal, diagonal, vertical etc for lines of letters)
- Blur elipse is from the subjects point of view
- subject behind- so flips
go over???
What does a point object appear as in general?
blur elipse in presence of astigmatism.
When does point object appear as a blur circle?
when the DLC falls on the retina or a line focus if were at one of the foci principle meridians
What can astigmatism be considered as?
Astigmatism can be considered as two different degrees of spherical ametropia along the principle meridians
What is astigmatic blur eclipses (major axes of elipse )?
are perpendicular to the meridian that is closest to focus- reforged to paradox to astigmatism
What is a simple myopic astigmatism ?
One meridian focus lies on the retina and the other in front of the retina
An eye with simple myopic astigmatism views a point source. The image on the retina is:
a line
What type of astigmatism is represented by the prescription -1.00/-1.75 x35?
compound myopic astigmatism
What type of astigmatism is represented by the prescription +0.75/-1.25 x170?
Mixed astigmatism
What does The length of the astigmatic line depends on?
(p x Ast)/Fe,theta
An astigmatic reduced eye has principal meridian powers of +59D and +63.5D. What is the Dioptric location of the disc of least confusion?
+61.25D
Calculate the size of the disc of least confusion if an eye has principal meridian powers of +60D and +63.5D and the pupil size is 4mm:
0.113mm
An astigmatic reduced eye has an ocular refraction of -0.50/-1.50 x10. Calculate the major and minor axes of the blur ellipse if K’=+60D and the pupil size is 5mm:
minor: -0.042mm; major: -0.167mm
