VS 117 LABORATORY III: BINOCULAR ACCOMMODATION:
(CONSENSUAL AND ANISO ACCOMMODATION)
INTRODUCTION
In most situations, the accommodative response is equal (consensual)
in the two eyes, even when one eye is occluded. However, there
are situations (such as uncorrected anisometropia) in which the
accommodative stimulus in the two eyes is unequal. If the difference
is small (i.e., < 0.75 D), some individuals can differentially
accommodate using aniso-accommodation and clear both eyes images
at the near distance. In this lab, we will demonstrate the consensual
and aniso-accommodative response.
A Badal optical system is one in which an object can be moved
toward or away from the eye without changing the angular subtense
of the retinal image, yet still allowing a change of vergence.
This is accomplished by placing a convex lens in front of the
eye so the secondary focal point of the lens coincides with the
primary focal point of the eye's optical system (approximately
the spectacle plane: 1.5 cm from the eye).
The apparatus you will use for this experiment has two Badal systems,
one for each eye. Each system is mounted on an arm which is part
of a haploscope (a form of Wheatstone mirror stereoscope). Although
the haploscope part of the apparatus will not be used as such,
each arm provides a support for a moveable stigma (point light
source), a Badal lens, a lens holder with several cells, and a
half silvered mirror. Moreover, ability to rotate the arm around
an axis passing through the rotation center of the eye has certain
advantages which will become apparent later on.
Since the above mentioned stigma can be moved along the haploscope
arm, a subject can move the stigma to a position of conjugacy
with the retina. Therefore, the location of the stigma can indicate
the conjugate focus of a given eye's optical system, and from
this conjugate focus (CF, which is the reciprocal of stigma distance
in meters) the accommodative response (AR), or the refractive
error (RE) can be calculated according to the relation:
CF = RE + AR + L (All units are in diopters.)
where CF = conjugate focus of stigma
RE = refractive error (RE = positive for myopes and negative for
hyperopes)
AR = accommodative response
(AR is positive if accommodation increases the eye's dioptric
power, and negative if it decreases the eye's dioptric power.)
L= auxillary lenses in the spectacle plane*
* The spectacle plane is assumed coincident with the first focal
plane of the eye, and, throughout this experiment, accommodative
response, refractive error, and any accessory lenses put in the
cells will be regarded as having their effects in the spectacle
plane, i.e., there will be no need to take account of positional
power as far as RE, AR, and L are concerned.
The diagram below is a top view of the optical components of
one of the two Badal optometers, showing its relation to the right
eye of a subject.
For the laboratory Badal optometer, the following data apply:
d1 = s.r. - k (s.r. is the scale reading on haploscope arm)
d2 + d3 = 10.0 cm (for a P = +10 D lens)
d2 + d3 = 12.5 cm (for a P = +8 D lens)
When a setting is made with the optometer, the location of the
stigma is determined from the centimeter scale on the haploscope
arm (d1 = s.r. - k). Stigma location (d1) can then be transformed
to a vergence value in diopters with respect to some specific
location such as the familiar spectacle plane.
Additional useful parameters for this lab are:
x = stigma distance from Badal lens anterior focal point
k= scale correction for subject settings (i.e., offset of scale
reading from lens focal length)
s.r.= scale reading
f = focal length of Badal lens (0.10 meters)
d1= stigma distance to Badal lens = s.r. - k
V = optical vergence subtended by stigma at spectacle plane
AD = 1/TD - L - RE
AD = accommodative demand (AD is positive if the required accommodation
must increase.)
TD = target distance (TD is positive for real targets.)
L = lens power
RE = refractive error (RE = positive for myopes and negative for
hyperopes.)
In the above diagram, a Badal system is shown on-line, i.e., without
the half-silvered mirror so the optical relations can be seen
more easily. The final path of the refracted ray is not shown,
because we are presently concerned with the relationship between
the incident vergence at the spectacle plan (V) and stigma (M)
location. Note, in this illustration, that M is closer to the
lens than the focal point by the distance X' from the secondary
focal point of the Badal lens. According to the Newtonian relation,
(1) xx' = ff'; but f = f' (lens in air)
(2) therefore, xx' = f2 = P12
Also, since we are interested in the Dioptric incident vergence
(V) at the spectacle plane we note that:
- 1x' = V, or x' = - 1V
substituting in (1), - xV = P12 , and solving for -V
- V = xP2
If M' is conjugate to the retina, it follows that
- V = CF which means that the incident vergence at the spectacle
plane equals the reciprocal of the conjugate focal distance in
meters (sign reversed).
So, given P2, which is constant for a given Badal system,
(3) CF = xP2
FOR A +10 D LENS:
From Fig. 2:
x = f - d1 = 0.10 m - d1 m
Since d1 = s.r. - k
x = 0.10 - (s.r. - k) = 0.10 - s.r. + k = .10 + k - s.r. (all
units in meters)
P2 = 1/f2 = +1/((0.1m)2) = +100D2
Substituting in (3):
CF = (0.10 + k - s.r) * 100 (where CF is in units of 1/m or D,
and all other variables are in units of meters)
(4a) CF = (10 + k - s.r.) (where CF is in units of 1/m or D,
and all other variables are in units of cm)
Since the vergence change within the lens focal length is linear
such that each 1cm increment of the 10 cm focal length corresponds
to 1D of the total 10D lens power,
CF = 10D - (d1 / 1.0) (d1 = s.r. - k) (d1 is in cm)
FOR A +8 D LENS:
From Fig. 2:
x = f - d1 = 0.125 m - d1 m
Since d1 = s.r. - k
x = 0.125 - (s.r. - k) = 0.125 - s.r. + k = .125 + k - s.r. (all
units in meters)
P2 = 1/f2 = +1/((0.125m)2) = +64D2
Substituting in (3):
CF = (0.125 + k - s.r) * 64 (where CF is in units of 1/m or D,
and all other variables are in units of meters)
(4b) CF = (12.5 + k - s.r.) * 0.64 (where CF is in units of
1/m or D, and all other variables are in units of cm)
Since the vergence change within the lens focal length is linear
such that each 1.56cm increment of the 12.5cm focal length corresponds
to 1D of the total 8D lens power,
CF = 8D - (d1 / 1.56) (d1 = s.r. - k) (d1 is in cm)
To summarize, therefore, the two relationships that apply to
the present experiment are equation (4a) and (4b) above, for finding
conjugate focus in reciprocal meters, and the general equation
CF = RE + AR + L relating reciprocal conjugate focus to refractive
error, accommodative response, and any lens in the spectacle plane.
ILLUSTRATIVE EXAMPLES
(These should be studied before analyzing your data.)
Assume k = 5 cm
1. An ametropic observer with accommodation relaxed sets the sigma
at a scale reading of 13.0 cm. As stated earlier, when a setting
is made, the sigma is conjugate to the retina. Since zero accommodation
is in force we can determine the refractive error of the test
eye from the relations discussed earlier.
From equation (4):
CF = (10 + 5 cm - s.r. cm) m-1
= 15 - 13 = 2.0 m-1
From equation relating CF to RE, AR, and L:
CF = RE + AR + L
+ 2.0 = RE + 0 + 0 Therefore, the test eye is + 2.0 D myopic
2. A 1.0 D myopic eye fixates a near target through (not by reflection)
the half-silvered mirror. When the sigma is set for conjugacy
the scale reading is 12.2 cm. How much accommodation is in force,
i.e., what is the accommodative response?
CF = (10 + 5 cm - s.r. cm) m-1
= 15 - 12.2 = 2.8
2.8 m-1 = RE + AR+ L = +1.0 + AR + 0
2.8 - 1.0 = AR = + 1.8 m-1 Therefore, the accommodation in force
is +1.8 D *
* The sign is significant, because, under some physiological and/or
environmental conditions accommodative response can take on negative
values relative to some initial accommodative level.
3. An emmetrope views a distant target through the half-silvered
mirror. A -5.00 D lens is placed in the spectacle plane to stimulate
accommodation. The scale reading for conjugacy of stigma to the
retina is 16.0 cm. Calculate the amount of accommodation actually
used (accommodative response).
CF = (10 + 5 cm - s.r. cm) m-1 = 15 - 16 = -1.0 m-1
-1.0 = RE + AR + L = 0 + AR + (-5.0) = 0 + AR - 5.0
AR = 5.0 - 1.0 = +4.0 D Thus, the actual accommodation in force
under the given condition is +4.0 D.
4. Calculate the scale reading for conjugacy of stigma to retina
when a -4.0 D hyperopic eye views a distant target without any
accessory lens in the spectacle plane. (Assume accommodative response
equals zero. Therefore, the target will appear blurred to the
subject.)
CF= (10 + 5 cm - s.r. cm) m-1 = RE + AR + L
15 - s.r. = -4.0 + 0 + 0
15 + 4.0 = s.r. = 19.0 cm for the given conditions
EXPERIMENT
APPARATUS: Badal apparatus, distance Snellen chart, reduced
Snellen chart, optical bench, trial lens set, meter stick.
METHOD: Use two members of your group as subjects; each subject
should be an emmetrope or have minimal refractive error (less
than 0.50 D, if possible). Refractive states of both subjects
must be known since the amount and kind of refractive error is
involved in calculating accommodative response. Perform PART I
through PART IV with the first subject, then repeat those parts
for the second subject.
PART I. Record subject's spherical correction (in diopters).
Set each haploscope arm at zero degrees, and lock the clamp screws.
Set interaxial distance equal to subject's PD. Have subject place
his/her head in the head rest and direct her/him to fixate the
3 meter target. An assistant adjusts the chin rest, while looking
through the sighting device, to bring subject's eyes to the proper
height in front of the lens cells. Next, adjust the forehead rest
to move the head forward or backward until the apex of each cornea
is in line with the sighting device for each eye. These adjustments
will place the corneas at standard distance (approx. 14 mm) from
the middle lens cell plane. Have the subject move the stigma along
the arm to determine if considerable horizontal or vertical motion
of the stigma image is perceived. Stigma image motion may be minimized
by increasing or decreasing the interaxial setting a millimeter
or two. Ideally there should be no apparent horizontal or vertical
motion of the image as the stigma is moved along the arm.
Move the 3 meter chart laterally so the projected position of
the sigma image, as viewed through the half-silvered mirror, falls
on the black paper attached to the chart. This increases the contrast,
making the stigma image easier to see. Note that an occluder covers
the far side of the left hand half-silvered mirror. This occluder
must be left in place from PART I through PART III. The right
eye will be looking at the Snellen chart, but each eye will see
its own stigma image. The near surface of the left half-silvered
mirror is not covered.
While fixating some letter near the black background on the Snellen
chart, move the stigma along the right arm until the spot of light
appears clearest, i.e., until the edges are sharpest. Be careful
to maintain fixation on the letter while doing this. Do not attempt
to "follow" the small light, because if you accommodate
for this light your results will be inaccurate. Adjust the stigma
before the right and left eye until both stigmas are simultaneously
clear. Bracket each stigma slightly farther and slightly nearer
than the optimal focus point. Choose the midpoint of this range
as the stigma location. Record the position of each stigma (s.r.)
as read from the scale on the haploscope arm. Repeat until four
pairs of readings have been obtained.
PART II. Place the reduced Snellen chart a distance
of 50 cm from the middle lens cell. Have the subject carefully
fixate the smallest readable letters while he/she makes four settings
of the right-hand and left-hand stigmas. Observe the same precautions
advised in Part I. Record the above settings on your data sheet.
PART III. Place a -2.0 D lens in the right middle lens
cells. Have the subject fixate the reduced Snellen chart placed
in the same position as for Part II, and record four stigma settings.
PART IV. Differential (aniso) accommodation. Adjust
the chin rest to bring the eyes to the proper level in front of
the lens cells. Remove the occluder and the -2D trial lens from
in front of the left eye and view the near target at 25 cm binocularly.
Make four settings of both stigmas. Now place a +0.5 lens in the
right middle lens cell, and make four additional settings of both
stigmas. You can compare the difference in the accommodative response
of the two conditions to estimate whether aniso-accommodation
occurred.
REPORT
For this lab, each group should turn in a single report containing
the following:
A. Practice problems. (Each person should submit individual solutions
as part of the group report.)
B. Data analysis. (Only one data analysis is required for the
group.)
C. Data sheet. (Only one data sheet is required for the group.)
A. PRACTICE PROBLEMS
1. The average scale reading is 16.0 cm for a 1.5 D myopic eye
fixating a distant target. The trial lens is -3.0 , and the Badal
lens power (P) equals +10D. What is the accommodative response
(AR)? Assume k = 5cm.
2. Both eyes of a subject are 2.0 D myopic. The right eye fixates
a chart 40 cm in front of the spectacle plane through a -3.0 D
trial lens. The Badal lens power (P) equals +10D. The left eye
has a +1.0 D trial lens, and the far side of the left half-silvered
mirror is covered. Therefore, the subject cannot see the 40 cm
target with the left eye, but can see the left stigma. Assume
k = 5cm.
a) If the accommodative response of each eye equals 2.5 D, what
are the stigma settings (d1) for each eye?
b) What is the accommodative demand (AD) for the right eye.
c) Is the right eye over-accommodating or under-accommodating
for this stimulus? By how much?
B. DATA ANALYSIS
PART I. a) Calculate the accommodative response (AR) for each
eye. (Compare for both subjects.)
b) Were the results between the two eyes consensual?
PART II. a) Calculate the accommodative response (AR) for each
eye. (Compare for both subjects.)
b) Were the responses between the two eye consensual?
c) How much higher was this response than that obtained in PART
I?
d) What was the accommodative demand (AD)?
e) Theoretically, how much accommodative response should have
occurred if the accommodative response (AR) equaled the accommodative
demand (AD)?
PART III. a) Calculate the accommodative response (AR) for
each eye. (Compare for both subjects.)
Did the results differ from PART II?
b) What was the accommodative demand (AD)?
PART IV. a) Calculate the accommodative response (AR) for each
eye. (Compare for both subjects.)
b) Did aniso-accommodation occur for this condition?
Data Sheet for Lab #1