Theses, Dissertations and Capstone Projects

Pacific University Pacific University

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College of Optometry Theses, Dissertations and Capstone Projects

Spring 1968

Comparison of the subjective cylinder rock and cylinder power

Comparison of the subjective cylinder rock and cylinder power

method with the conventional Jackson cross cylinder technique

method with the conventional Jackson cross cylinder technique

Saul Mendelsohn

Pacific University Kenneth Silbernagel Pacific University Douglas Smith Pacific University

Recommended Citation Recommended Citation

Mendelsohn, Saul; Silbernagel, Kenneth; and Smith, Douglas, "Comparison of the subjective cylinder rock and cylinder power method with the conventional Jackson cross cylinder technique" (1968). College of Optometry. 295.

https://commons.pacificu.edu/opt/295

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Comparison of the subjective cylinder rock and cylinder power method with the

Comparison of the subjective cylinder rock and cylinder power method with the

conventional Jackson cross cylinder technique

conventional Jackson cross cylinder technique

Abstract

Abstract

Comparison of the subjective cylinder rock and cylinder power method with the conventional Jackson cross cylinder technique

Degree Type Degree Type Thesis

Degree Name Degree Name

Master of Science in Vision Science Committee Chair

Committee Chair D.T. Jans

Subject Categories Subject Categories Optometry

This thesis is available at CommonKnowledge: https://commons.pacificu.edu/opt/295

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l

·

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11

.

-

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COMPARISON

OF

THE

SUBJECTIVE

CYLINDER ROCK AND

CYLIND

E

R POWER

METHOD WITH

THE CONVENTIONAL

JACKSON

CROSS

CYLINDER TECHNIQUE

by

Sau

l

Mendelsohn

Kenneth Silbernagel

Douglas Smith

Submitted in Partial Fulfillment

of the Requirement for the Degree:

Doctor

Approved

--- ···· · -··- - - - -- --- ---·-·- - - - -- - -- ·-

ACKNOWLEDGEMENTS

We are grateful to Dr. Jana for giving ua advice in

the planning of the study, and to the twenty-three persona

who were willing to give of their time to act as subjects

for the project.

~·

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TABLE OF CONTENTS

P

U

RPO

S

E

1

REVIEW OF THE LITERATURE ---

2

PROCE

D

URE AND APPARATUS ---

3

ORGANIZATION OF THE DATA ---

6

STATISTICAL ANALYSIS ---

16

C

O

NCLUSIONS ---

19

REFERENCES ---·---·---

20

..

.

•

c

~

1

PURPOSE

~

The purpose of this study is to compare the Jackson Cross

Cylinder method of determining axis and power with the Subjective

Cylinder Rock and Cylinder Power method. We are interested in

knowing how,consistently the Subjective Cylinder method compares

favorably with the Jackson Cross Cylinder method, and which method

shows better resolution acuity. We would like to know if the

Subjective Cylinder method can justifiably be used in the clinical

routine as a basis for cylinder axis- and cylin~er---power prescription •

~I

2

REVIEW OF THE LITERATU~E

W. B. Lancaster was the first to write on the "rocking

· ... ne cylinder" method of determining the subjective cylinder axis.

I am sure that the method md ,been used before he originally di scussed the techniqu~ in his paper on the dial tests. Dr.

1

Beach , Chief Ophthalmologist at the Staff Main& Eye and Ear Infirmary, discusses the technique in his book on t'efraction1

and calls i t a fast and accurate test, however he presents no data showing how i t compares with other methods. A survey of the literature on the subjective cylinder power and cylinder axis technique showed that apparently there has never been done an analysis to compare the subjective cylinder rock method with any ot'her method.

1

Beach, Sylvester

J.,

Prin6iples·of

Refra~tion,

the

c.v.

Mosby Co.,

1952,

pgs.

78-80.

·'

.

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\...~

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2

·- - -- - -- - -- - -

---..

----

3

-

---

PROCEDURE AND APPARATUS

We are interested in comparing cylinder power ₁ cy.linder axiE, and acuity difference obtained by using the Jackson Cross Cylinder Technique and the Subjective Rock Technique. All comparisons and testing ~re done monocularly.

The routine followed is as discussed below: 2

A. Conventional Jackson Cross Cylinder method: The clock dial is run in the conventional manner with the appropriate amount of plus to obtain cylinder axis and cylinder power. Plus is reduced until the subject first reports the letters on the green side of the red-green chart to be more clear, and the Jackson Cross Cylinder axis and power determination is made. The final sphere power is obtained by adding plus and then reducing until .the most plus for best visual acuity is obtained.

B. Subjective Cylinder Rock and Cylinder Power Method: All cylinder power is removed from the phoropter, and plus is added until the 20/40 line is definitely blurry, and then plus is redu~ed uritil the letters on the green side of the red-green chart are clearest. At this point -0.50 cylinder axis

45°

and +0. 25 sphere is added to the phoropter. The 20/20 line is projected on the chart and th~ cylinder axis is rocked, not the points at which the subject reports "first blur". The cylinder axis is placed mid-way between these blur points. The cylinder power is then rocked in half diopter st eps, and

placed mid-way between the points which the subject reports as "not as clear", placing the lesser amount of cylinder in

~·

.

the phoropter if the midpoint is an eighth diopter step. Plus is added until the 20/40 line is blurry and then reduced

until the point at ~hich the most plus for best visual acuity is reached.

Barish, Irvin M., Clinical Refraction, The Professiona1:Press Inc.,

1954,

pgs.

285-289.

..

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_

·it

-

-

----~·----

c.

Acuity Comparison:

Acuity comparisons of the two methods

were made using an apparatus with two vertical threads, one

stationary and one moveable.

The black threads, placed in

front of a white illuminated background, were first placed

one directly behind the other so th13-t ()nly one thread is

perceptable.

A wing nut with one end marked blue, placed

t

o turn over a scale marked in one sixteenths of a turn, is

turned so as to move the moveable thread from behind the fixed

thread so as to create a small space between the threads.

The patient is asked to say "two" when he first sees two

threads.

One turn of the wing nut is 1.27 mm.

The distance

from the acuity resolution apparatus to the subject is

538

em

+

10 em.

Knowing these figures, we were able to convert the millimeter

thread separaration into minutes of arc subtense.

To eliminate the practice effect, the first two resolution

;

acuity readings were taken thru the subjective lens complex,

the next two thru the JCC complex, the fol

l

owing two thru the

subjective rock complex, and the last two thru the JCC complex.

A total of four resolution acuity readings were taken for each eye and

aver.aged.

The averages were used in the calculations.

'

.

The resoiution acuity apparatus is diagramed on the

following page

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DIAGRAM OF RESOLUTIC1N APPARATUS

- ," - - - ---1--~/'-'L--_ _ _ _ _ _

r-~- --.

I

5

t.o..•i •'j not

./ ( j ·tc:cn o.

I

/f

j,. d..7

17/n;)

!mii:ll.U

I:tC

rl

1

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~~

I

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:

~

--~

~

-

=-

-=~

~

-

~

~~~

.

~

~~~~~~-

JJ~

i

~--~

I

---·-~···~... --~·---··· ··---·~~---

-

6

Organization of the Data

The majority of the subjects were between the ages of

twenty and thirty.

Twenty three subjects were tested.

The

•

age distribution is as follows:

AGE

NUMBER OF SUBJECTS

0 - 10 years

0

11-

20 years

2

21-

30 years

18

31-

40 years

3

Two of the subjects were females, the rest males.

Table

I,

page 7, is a tabulation of the raw data.

Scattergramsi and

II

compare subjective cylinder power

and JCC cylinder power for the right eye and left eye respectively,

pages

9

and 10.

Scattergrams

III

and

IV,

pages

.

11

and

~2,

compare the

cylinder axis in degrees for the right eye and left eye

respectively.

Scattergrams

V

and VI, pages 13

'

and

14

9

compare resolution

acuity in

minutes

6f

arc

·

for the right and l

;

eft eyes respectively

Table

II

shows an analysis of the data

on a

percentile basis,

page

15.

Table

III,

page 17j shows the results of the statistical

analysis for cylinder power and cylinder axis.

Table IV, page

i6,

~hows

the

results of the statistical

analysis

for

resolution acuity •

.

·

I;

7

·

TABLE I

RAVJ DATA

Su

b

j

e

ct Jackson Cros

s

Subjective Cylinder

Average of

Aver

c;.

ge of

Numb~r

_Cylinder

_Rock

_Resolution

_Resolution

Acuities in

Acuities in

Millimeters

Minutes of

Arc.

JCC

Rock

JCC

Rock

1. +1.75 -

0

.75 X 5

+1.75 -0.75 X 175

0.95

0.84

0.61 0.54

+

1.

50

sph

+1.50 sph

2. -

0

.75 -0.25 X 165

-1.00 -0.25 X 170

1.16 1.10

0.74 0.70

-

0

.75 -

0

.

2

5 X 170

-1.25 -0.25 X 180

1.22 1.05

0.78 0.67

3· -6.25 -

0

.

5

0 X 65

-6.25 -0.50 X 60

'

0.67 0.66

0.43 0.43

-5.25 -

0

.50 X 70

~5:oo

-0.50

X 85

o.62 0.69

0.40 0.44

4. -6.00 -1.75 X 35

-6.00 -1.25 X 25

1.24 1.56

0.79 1.00

-

5

.75

-

2.00 X 180

-6.0

0 -

1.50 X 170

1.49 1.22

0.95

0

.78

5· +0.25 -0.50 X 180

pl

-

0.75 X 175

1.72 2.08

1.10 1.30

\...

_6.

₎

-0.25 -0.25 X 165

_{_ 3· 50 -0.25 X 90}

-0.50 -0.50

_{-4.00 -0.75 X 180}

.

X 165

2.30 1.81

_{0.91 1.11}

1.47 1.16

_{0.58 0.71}

-

3

.25 -0.75 X 180

-3.50 -0.75 X 180

1.00 0.96

0.64 0.61

7-

-

2.

25 -1.00 X 175

-2.75 -1.00 X 175

2.01

.

1.39

1.28 0.89

-2

.

• 75 s

p

h

-2.75 sph

><

u.

-1.75 -

0

.25 X 90

_{-1.75 -0.50 X 75}

1.33 1.44

·.

0.85

0

.

92

-2.25 -

0

.25

X 45

-2.00 -0.50 X 45

·

1.41 1.37

0.90 0.88

9· +0.50 -0.50 X 115

+0.25 -0.50 X

1

05

1.20 ll.14

0.77 0.73

+0.25 -0.25 X 75

pl -0.50 X 70

1.00 1.28

-·

o•64

.

0.82

10.

-

-2.25 -0.50 X 20

-2.50 -0.50 X 30

0.75 1.12

0.48 0.72

-1.75 -0

.

75 X 10

~~.-50

-0.75 X

,1

6

0 •

.

86 0.55

~· l

0.55 0.35

11. +1.25 -1.25 X 100

+1.25 -0.75 X 70

2.00

,

2.02

1.28 1.29

+2.50 -0.75 X 56

+3.00 -0.50 X 55

.

3

_..

.

11 2.

,

96

.

·

1.98 1.89

12. -

2

.25 -0.50 X 7

-2.25 -0.75 X 3

I

1.)9

.

2.04

0.89 1.31

-3.50 -0.75 X 180

-3.75

'

-0.75 X 170

~

3.11 2.96

1.99 1.89

13. -2.50 -1.00 X 180

-2.24 -1.25

.

X 5

1.26

'

,

1.16

0.81 0.74

-

3

.00 -0.75 X 160

-2.75 -0.75 X 16

0

~-

.

,

0.63 0.97

0.41 0.62

14. -3.50 -0.75 X 120

-3.50 -0.75 X 110

2.44 2.66

1.56 1.71

-3.25 -1.25 X 135

-3.25 -1.25 X 155

! •

1.

,

47

.

1.47

0.94 0.94

15. +0.25 -1.25 X 172

+0.25 -1.50 X 175

1.67 1.60

1.07 1.02

pl -1.75 X 53

p1 -1.75 X 50

1.75

.

1.71

1.12 1.09

•,

.

.

.

.

'

.

•'

TABLE I (Continued)

Subject Jackson Cross

Number Cylinder

16. -4.j0 -0.75 X 105

-5.25 -1.25 X 45

1

7.

-2.

00 -

0

.

50 X 135

pl

-

0.50

X 30

18

. -

3.25 -1.25 X 90

-3.00 -1.25 X 90

1

9

.

-2

.25 -0.

5

0 X 1

30

-

3

.00 -0.50 X 45

20. -2.25 -1.00 X 137

-3.00 -1.25 X 35

21. -1.00 -1.25 X 85

-0.75 -1.00 X 8o

22. +2.50 -2.25 X 178

·

+3.00 -1.00 X 68

23. -0.75 -0.75 X 108

-0.50 -0.50 X 62

.

Subjective Cylinder

.Rock

-4.50 -0.75 X 100

-5.25 -1.25 X 45

-2.00 -0.75 X 135

pl -0.50 X 30

-3.25 -1.50 X 85

-3.23 -1.25 X 90

-

2.2

5

-

0

.5

0 X 1

3

0

-3.00 -0.75 X

20

-2.25 -1.25 X

-3.00 -1.25 X

;:.1.00 -1.25 X

-0.75 -1.50 X

+2.50 -2.25 X

+3.00 -1.00 X

-1.00 -0.75

X

~l.OQ

-0.50 X

..

.

I

130

30

87

85

178

70

112

6o

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8

Average of Average of Resolution Resolution Acuities in Acuities in Millimeters Minutes of

Arc.

JCC Rock JCC Rock

2.47 1.91

1.58 1.22

2.24 1.93

1.43 1.23

1.98 1.87

1.27 1.19

2.81 2.81

1.80 1.

80

2.00 2.00

1.28 1.28

1.95 2.00

1.25 1.28

1.

92

1.72

1.23 1.10

1.62 1.60

1.13

1.03

1.72 1.72

1.10 1.10

·

1.62 1.71

1.04 1.09

,

.

"

.

l

• I

12-188 Sea ttergram I

10 M:lili1netcn; to the Cc:ntirnetcr

Scattergram II 12-188

"'·

10 l\fillinH'lCfS tO the C~nt iutctcr

12-1t'>

1.0 Millhnctcrs to the C''n1itnctcr

Scattergram III

!

11

12-188

0

~

I

li

i

P

',1; I

1 o Milffmctcrs to the ·ccntiinctci"---

Scattergram IV

. I

I rll

! ,

-1-1++1 [

I

I

l..2.

Ji+IH-H-I+H-1

!

I I

,. ,

·"

I •·· I f !

! I

, 'I

!•; !·

·j· .. !lH• 11-1-111-ft+H

. i

11-H-H-H

Scattergram V

L::.-i06

10 1\/iilbn·tl·rcrs to the Ccntin1ctcr

10 Millimeters to the Cciltimctcr

---

'l

.

.

TABLE II

₁₅

Analysis of the Data

Cyllinder

~

91%

of the subjective rock cylinder axis findings were

within 15° or less of the JCC axis findings.

86%

of the subjective rock cylinder axis findings

were within 10° or less of the JCC axis findings.

65%

of

the subjective rock cylinder axis findings were

within 5° or less of the JCC axis findings.

Cy::;_inder Power

23% of the cylinder power subjective rock findings

showed 0.25 diopter

more

cylinder power.

7%

of the cylinder power subjective rock findings

showed 0.50 diopter more cylinder power

2% of the cylinder

power

subjective rock findings

showed

0.25 less cylinder

power.

5%

of the cylinder

power

subjective

.

rock findings showed

0.50 less cylinder power.

63% showed no cylinder

power

change from the JCC

30% showed more cylinder

power than

the JCC

9%

showed less cylinder

po

wer

than

the JCC

88%

~hawed!

0.25 cylinder

'

pbwer or less change from

the JCC

•

Resolution Acuity

60% showed better subjective rock resolution acuity

32% showed bett•r Jackson Cross Cylinder resolution acuity

8%

showed

no acuity difference.

Subjective resolutidn acuity is better than JCC resolution

acuity at the 12% level of significance.

I r I ~~

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-·

--

-

·-

-.-

··-·

-

-

-

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__

=---~---_..:.---

16

STATISTICAL

ANALYSIS

Th

e

formulas used in statistical analysis are as follows:

3

Me

an

:

M

=

EX

_Where

_M

=

the arithmetic mean

N

E =

the sum of

X =

a value from the data

N

=

the total number of values

S

t

andard DeViation:

s

~

e.

.

··~

N-1

Where

s

=

the standard deviation

E

₌

t

h

e

s

um

of

2

a

deviation from the

.

x

=

mean squared

N

=

the total

·

number of values

Correlati

o

n Coeff

i

cient:

r

=

EXY

Where r

2

the correlation coefficient

E

=

the sum of

X

=

a deviation from the mean

Mx

~

---

''

---

I

\

\

L

L

J

17

TABLE III

The Results of the Statistical Analysis are as follows:

Means:

Power of ~ cylinder in diopters

Jackson Cross Cylinder

O.D

_•

---

-0.84

o.s ---

_•

-0.76

Axis of the cylinder

i£

degrees

Jackson Cross Cylinder

O.D. ---

107.7

o.s ---

92.1

Standard Deviations:

Power

£1

~ cylinder in diopters

Jackson Cross Cylinder

o.n.

o.s.

0.063

0.062

~

£!

~ cylinder in degrees

Jackson Cross Cylinder

0 D

.

.

o.s

66.8

69.2

_---

Co:~:celation Coefficients:

l. 2.

3·

4.

power of power of axis of axis of

~---...

--

l , - .

0

.

D

_•

o.s.

O,D

0 •

o.s.

- -.,____.,..

___

__

,.

=

0.91

=

0.97

=

0.96

=

0.98

Subjective Cylinder Rock

O.D. ---

-0.90

o.s. ---

-0.76

Subjective Cylinder Rock

O.D. ---

lOB.3

o.s. ---

91.0

Subjective Cylinder Rock

o.n. ---

o.s. ---

o.o64

0.057

i

Subjective Cylinder Rock

O,D, ---

66.1

o.s. ---

70.3

J

~ ·.·

(

'

•t

I j

\.._..-

18

TABLE IV

Resolution Acuity in Minutes of Arc

Means:

Jackson Cross Cylinder Subjective Cylinder

Rock

Difference

o.n. ---

o.s. ---

1.02

1.14

---·----

O.D. ---1.05

-0.03

--- o.s.

---1.09 ---+0.05

Standard Deviations:

O.D.

o.s.

Jackson Cross Cylinder

0.12

0.24

Correlation Coefficients: 1.

o.n.

acuity:

o.90

2.

o.s.

acuity:

0.97

Subjectiv• Cylinder Rock

o.n~ -M-~---0.12

o.s.

~-::7'-.-~---0.23 ,r'

1 , .

I.

1

19

CONCLUSIONS

It may be concluded that the subjective cylinder rock

and cylinder power method of determining cylinder axis and power may justifiably be used in the clinical routine as a basis

for prescription of glasses.

The data and statistical analysis show that in

86%

of the cases the subjective cylirider axis will be within 10° of the Jackson Cross Cylinder axis, and that in

88%

of the

cases the cylinder power by the subjective rock technique will be within! 0.25 diopters. The resolution acuity findings on an eye to eye comparison basis slH>ws almost twicEt as many showing better resolution acuity by the subjective rock method than lower resolution acuity thru the cross cylinder technique. When comparing the resolution acuities on an bverall

' .

basis, as shown by the means, the data is slightly in favpr of the rocking method.

\,'

• . 0 • •

l

REFERENCES

l.~each, Sylvester J., Principles of Refraction, The C. V.

Mosby Co,

1952,

pgs.

7

8

-8o, 91-93·

2. Barish, Irvin M., Clinical Refraction, The Professional Press Inc.,

1954,

pgs.

285-289

3.

Roessler

&

Alder, Probability and Statistics,

w.

H.

Freeman and Co,

1964,

pg.

15B-159, 169-173.