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The Physics of Goldmann Applanation Tonometer
V. Srinivasan, MA, MS(Oregon, USA), Consultant (Retired),
Instruments Maintenance Laboratory, Aravind Eye Hospital, Madurai, India
The Goldmann applanation tonometer is the gold
standard for the measurement of Ocular pressure
(IOP) used in the diagnosis of Glaucoma. To
measure the IOP, the tip of the prism unit of the
tonometer is pressed against the cornea of the
patient. The cornea gets flattened (applanated)
uniformly. Then the cylindrical measuring drum
of the instrument is turned (adjusted) looking
through the eye piece of the slit lamp on which
the tonometer is mounted till a pattern of two
semicircles just touching each other as in Fig.1
appears. By the design of the instrument, in this
position the diameter of the flattened circle is
3.06mm and the reading on the drum against an
arrow in the instrument multiplied by 10 gives
the IOP in mm.
For a body of 1 gm weight the force is = 1 x 10-3
(kg) x 9.8 (ms-2) = 0098 N. When this force acts
on a circular surface of diameter 3.06 mm, the
pressure = 0.0098/π(3.06x10-3/2)2 = 1333 Pa
( N/m2), the same as the pressure of 10 mm of Hg.
F
A
B
Fig : 2
F1
Fig. 1 (This figure is illustrative only and
not drawn to scale)
Pressure is force per unit area. The unit of
pressure in SI Units is Pascal (1 Pa = 1 N/m2,
Newton per square meter). However in practice
for many applications the pressure is expressed
in height of mercury column in millimeter (mm
of Hg). The pressure of 10 mm of Hg = 10x10-3
(the height in meter unit) x 13.6x103 (density
of mercury in kg/m3) x 9.8 (acceleration due to
gravity m/s2) = 1333 Pa (N/m2).
The weight of a body is the force due to gravity
acting on it. Force is also measured in gram weight.
C
F
F2
D
Fig : 3
Thus an IOP of 10 mm of Hg is the same as
the pressure due to a gram weight acting on a circle
of diameter 3.06 mm.
Forces (weights) are measured (compared)
using a balance. The horizontal beam balance
(Fig 2) is well known. The IOP measured with
the patient seated in front of the slit lamp acts
horizontally. The restoring force for measuring
Vol. XIV, No.4, October - December 2014
this horizontal force should also be horizontal
(Fig3). This is provided by the orientation of the
weights located inside the box of the tonometer.
The restoring force gets adjusted as the weights
inside the box get shifted with the turning of the
reading drum. To magnify the movement of the
support arm the principle of levers is used and
the measurement becomes more precise. By the
principle of moments F1 x CF = F2x DF. The arm
CF being more than DF any small change in F1
17
the IOP being measured, will be equivalent to a
large change in F2.
How are the prisms located inside the prism
unit? These are two narrow angled prisms located
one on top of the other with their apex pointing
in opposite direction. The angle of the prism
and their orientations (Fig. 4) are such that the
two semicircular images of flattened circle get
displaced sufficiently as in Fig 1 when the diameter
of flattened circle is 3.06 mm.
Fig.4 The orientations of two thin prisms and the ray diagram