8.2 - obliquely crossed cylinders

Question 1

What is an orthogonal axes?

Answer 1

2 cyls from a trial case with axis that are at right angles to each other
-obliquely crossed cylinders

Question 2

What are obliquely crossed cylinders in axes that are parallel/perpendicular to each other (orthogonal axes) EXAMPLE?

Answer 2

-2.00 cyl lens with a vertical axis and 0.00 at horizontal
+1.00 cyl lens with a horizontal axis and 0.00 at vertical
0.00/-2.00 x 90
0.00/+1.00 x 180
-Can simply put these together
+1.00/-3.00 x180
-This can suggest that we can add together cyls

Question 3

If the powers are parallel or perpendicular to each other ?

Answer 3

you can add the powers together

-using power crosses to make it work properly

Question 4

What are the obliquely crossed cylinders in axes that are not orthogonal -EXAMPLE?

Answer 4

0. 00/-1.00 x 180 obliquely crossed with
1. 00/-2.00 x 45
   - ANSWER: -0.40DS/-2.24DC X 32
   - The sph , cyl and axis can not be added together as they are components that are not independent of each other

Question 5

How do we work out obliquely crossed cylinders?

Answer 5

Put lenses in focimeter to measure the values
-represent this in power cross cyl form
Trial case lenses
\+1.00DC X 180
\+2.00 X 45
IN FOCIMETER
\+0.50D ALONG 36
\+2.85 ALONG 126

MEASURED: +2.85/ -2.35DC X 126
Theoretical : +2.62DS/ -2.24DC X 122
…

Question 6

What is The Jackson cross-cylinder (JCC)?

Answer 6

-helpful in refining and diagnosing astigmatism and correcting both the power and axis of the cylinder we prescribe

Question 7

What is the JCC equipment like?

Answer 7

• 2 cylinders placed at right angles to each other
• come at different powers - the lowest power is +0.25 and -0.25 cyl lens placed right angles to each other
• The markings show axes values for the powers - can come in higher powers to

Question 8

What is the sph/cyl form of the +0.25 cyl in the JCC? and what is the BVS?

Answer 8

+0.25DS / -0.50DC X 45

BVS= 0.00DS (AS +0.25 + -0.25)

Question 9

What does the cross cyl of the JCC do?

Answer 9

Doesn’t change the sphere component at all but can change the astigmatism
-used to make changes of the power of cyl and axes of cylinder in place

Question 10

What colours on the JCC represent the + and -?

Answer 10

(-) red

(+) black

Question 11

What can obliquely crossed cyls have?

Answer 11

• any number of cyls with arbitrary axis orientations results in a single sphere/cyl
• Conversely a sph/cyl can be considered as a superposition of cyls

Question 12

What are power vector analysis?

Answer 12

• there are a number approaches can be taken
• can take a sph/cyl (negative form ) prescription and can change it into a form so can be added together!
• original work after stokes (1883)

Question 13

How do you convert to power vectors?

Answer 13

• idea is to rewrite normal negative prescription notation in a form that can be added together.
• goiung to take sph cyl and axis ( s , c , ⍺ ) and convert into 3 other quantities (M , J0 , J45 form ) - then can add components together
• can convert back into sph /cyl and axis!

Question 14

What are the power vector equations?

Answer 14

M = S + C/2 mean spherical equivalent
J0 = -C/2 Cos (2⍺) JCC axis 180
J45 = -C/2 Sin (2⍺) JCC axis 45

Now can add together different cyls

Question 15

What are the power vector properties?

Answer 15

-The power vector components M, J0 and J45 can be added together

Question 16

How to convert back into sph cyl axis?

Answer 16

S = M + √J0^2 + J45^2 
C = -2√J0^2 + J45^2
⍺ = 1/2tan-1 ( J45/J0)

Question 17

EXAMPLE

Find the resultant of +1.00DC x 180 and +2.00DC x 45

Answer 17

1- Convert into negative cyl form
\+1.00/-1.00 x 90
\+2.00/-1.00 x135
-Then convert to m j0 and j45 
-Then add them 
-Then convert back to sph cyl axis