Optical Instruments for Angular Measurement (Metrology)



This is an optical instrument used for the measurement of small
angular differences. For small angular measurements, autocollimator provides a very sensitive
and accurate approach. Auto-collimator is essentially an infinity telescope and a collimator
combined into one instrument. The principle on which this instrument works is given below.
O is a point source of light placed at the principal focus of a collimating lens in Fig. 8.30. The
rays of light from O incident on the lens will now travel as a parallel beam of light. If this beam
now strikes a plane reflector which is normal to the optical axis, it will be reflected back along
its own path and focussed at the same point O. If the plane reflector be now tilted through a
small angle 9, [Refer Fig. 8.31] then parallel beam will be deflected through twice this angle,
and will be brought to focus at O’ in the same plane at a distance x from O. Obviously 00′ = x
= 26. f, where f’\s the focal length of the lens.
There are certain important points to appreciate here :
The position of the final image does not depend upon the distance of reflector from the
lens, i.e. separation x is independent of the position of reflector from the lens. But if reflector
Principle of working of autocollimator
Principle of working of autocollimator.
is moved too much back then reflected rays will completely miss the lens and no image will be
formed. Thus for full range of readings of instrument to be used, the maximum remoteness of
the reflector is limited.
For high sensitivity, i.e. for large value of a; for a small angular deviation 8, a long focal
length is required.

Principle of Autocollimator.

A crossline “target” graticule is positioned at the
focal plane of a telescope objective system with the intersection of the crossline on the optical
axis, i.e. at the principal focus. When the target graticule is illuminated, rays of light diverging
from the intersection point reach the objective via a beam splitter and are projected from the
objective as parallel pencils of light. In this mode, the optical system is operating as a
A flat reflector placed in front of the objective and exactly normal to the optical axis
reflects the parallel pencils of light back along their original paths. They are then brought to
focus in the plane of the target graticule and exactly coincident with its intersection. A
Reflected beam when reflector is square to beam
Reflected beam when reflector is square to beam
■ Reflected beam from tilted reflector
proportion of the returned light passes straight through the beam splitter and the return image
of the target crossline is therefore visible through the eyepiece. In this mode, the optical system
is operating as a telescope focused at infinity.
If the reflector is tilted through a small angle the reflected pencils of light will be
deflected by twice the angle of tilt (principle of reflection) and will be brought to focus in the
plane of the target graticule but linearly displaced from the actual target crosslines by an
amount 28 x f.
Linear displacement of the graticule image in the plane of the eyepiece is therefore
directly proportional to reflector tilt and can be measured by an eyepiece graticule, optical
micrometer or electronic detector system, scaled directly in angular units. The autocollimator
is set permanently at infinity focus and no device for focusing adjustment for distance is
provided or desirable. It responds only to reflector tilt (not lateral displacement of the reflector).
This is independent of separation between the reflector and the autocollimator, assuming no
atmospheric disturbance and the use of a perfectly flat reflector.
Many factors govern the specification of an autocollimator, in particular its focal length
and its effective aperture. The focal length determines basic sensitivity and angular measuring
range. The longer the focal length the larger is the linear displacement for a given reflector
tilt, but the maximum reflector tilt which can be accommodated is consequently reduced.
Sensitivity is therefore traded against measuring range. The maximum separation between
reflector and autocollimator, or “working distance”, is governed by the effective aperture of the
objective, and the angular measuring range of the instrument becomes reduced at long working
distances. Increasing the maximum working distance by increasing the effective aperture then
demands a larger reflector for satisfactory image contrast. Autocollimator design thus involves
many conflicting criteria and for this reason a range of instruments is required to optimally
cover every application.
Air currents in the optical path between the autocollimator and the target mirror cause
fluctuations in the readings obtained. This effect is more pronounced as distance from
autocollimator to target mirror increases. Further errors may also occur due to errors in
flatness and reflectivity of the target mirror which should be of high quality.
When both the autocollimator and the target mirror gauge can remain fixed, extremely
close readings may be taken and repeatability is excellent. When any of these has to be moved,
great care is required.

Laser Interferometer.

With laser interferometer it is possible to measure
length to an accuracy of 1 part in 106 on a routine basis. With the help of two retro-reflectors,
placed at a fixed distance, and a length measuring laser interferometer the change in angle
can be measured to an accuracy of 0.1 second. The device uses the Sine principle. The line
joining the poles of the retro-reflectors makes the hypotenuse of the right triangle. The change
in the path difference of the reflected beam represents the side of the triangle opposite to the
angle being measured. Such laser interferometer can be used to measure an angle upto ± 10
degrees with a resolution of 0.1 second.
The principle of operation is shown in Fig. 8.33.
Interferometric measurement of angle
Fig. 8.33. Interferometric measurement of angle.

Photoelectric Microptic Autocollimator.

Photoelectric setting makes
measuring and checking by autocollimator far simpler and faster. Micrometer adjustment is
provided for setting, but coincidence of setting graticule and target image is detected photo-
electrically, and shown on a meter as a null reading. This provides a high degree of sensitivity
and repeatability, also reducing eye fatigue to a minimum. The eyepiece is normally only used
to assist in initial setting-up.
Schematic diagram of Photo-electric autocollimator
Fig.8.34. Schematic diagram of Photo-electric autocollimator.
The photoelectric autocollimator is particularly suitable for calibrating polygons, for
checking angular indexing and for checking small linear displacements.
It can be used as a visual autocollimator, if required, and is available with a dark field
graticule as standard.
Fig. 8.34 shows a schematic of the operation of photoelectric autocollimator. It consists
of a vibrating slit, a photoelectric detector, electronic amplifier for magnified viewing on a

Operating Principle.

(Refer Fig. 8.35). The photoelectric detecting unit consists of
photocell and a vibrating slit which is attached to the micrometer screw. When the slit is
positioned so that it vibrates about
the reflected image, the intensity of
light received by the photocell will
vary. The output waveform is
amplified and fed to a frequency dis-
criminator and meter which, in
effect, indicates the asymmetry of
the waveform. When the slit is posi-
tioned so that it vibrates symmetri-
cally about the image the meter
indicates a null reading, and the
angular displacement of the target
mirror can be read from the
Schematic diagram of Photoelectric Autocollimator
Fig. 8.35. Schematic diagram of Photoelectric Autocollimator.
The autocollimator, with suitable reflecting surfaces or optical gauges, is capable of
calibrating straightness, flatness, squareness or division of the circle.

Automatic Position Sensing Autocollimators.

Automatic position sensing
autocollimators provide fully automatic setting and display. Angular displacement of the
reflector is displayed on a digital readout—eliminating any micrometer reading for setting or
Automatic autocollimators can be used in cramped positions where it could be impossible
to use a visual instrument, and no handling during measurement minimises the danger of
accidental autocollimator movement.
Instruments measure in one plane only. For measuring in a second plane perpendicular
to the first, the instrument is rotated through 90°. A dark field graticule is fitted as standard.
Accuracy is unaffected by normal mains fluctuations or lamp ageing.
Automatic autocollimators are ideal for the repetitive checking of production com-
ponents, and for continuously monitoring angular displacement of slow moving parts.

Operating Principle :

The vibrating slit image detecting system is similar to that
described for the photo-electric autocollimator, but in addition, the slit is electrically biased
across the field. The amplitude and polarity of the biasing signal is dependent upon the
misalignment of the slit with the return image. By this arrangement the slit is biased to the
position straddling the image, at which the misalignment is negligible. The current necessary
to hold the slit biased in this position is used to provide a direct angular reading on a digital

Autocollimator Accessories.

The full versatility of autocollimators can be
exploited by the addition of suitable accessories.
Levelling Base : It supports the autocollimator and enables it to be levelled to bring
its axis parallel to the surface being measured. It incorporates spring-loaded clamps and a
circular bubble level. Three pads are included for use under the foot screws. There is no
necessity to remove the autocollimator from the base after use as the autocollimator case is
constructed to take both items.
Surface Plate Stand : A multi-purpose stand of heavy duty construction for general
bench use, comprises ground cast iron surface plate, column and bracket. The autocollimator
clamping bracket has independent clamping and rotational adjustments, enabling the bracket
to be turned without disturbing the height adjustment.
Steel Reflector : A reflector must be
regarded as an integral part of any autocollimator
system. Successful autocollimation requires a
reflector of adequate flatness, reflectivity and
diameter. The parallelism of the faces is such that
negligible error is introduced when the unmounted
reflector is back mounted.
Use of autocollimator accessories
Fig. 8.36. Use of autocollimator accessories.
Mounted Glass Corner Reflector : This is used in conjunction with a reflector
carriage and mounted reflector for calibrating a surface plate. It enables several calibration
lines to be traversed without the autocollimator being moved, thereby saving setting-up time
and making the subsequent correlation of reading easier.
Steel Cube Reflector: It can be used as a general purpose reflector and for providing
a 90° angle standard in three planes, for setting or checking perpendiculars.

Microptic Autocollimator.

(Fig. 8.37). In this, a pair of target wires take place
of the point light sources as it is not convenient to visualise the reflected image of a point and
then to measure the distance x precisely. So a pair of target wires placed in the focal plane of
a collimating lens are il-
luminated from the back and
their image projected which
strikes a plane reflector and
the reflection of the image is
brought to a focus in the plane
of the target wires. The field of
view in the eyepiece in which
the wires and their images are
viewed simultaneously is
shown in Fig. 8.37.
Setting wires are placed
in the microscope unit and are
adjustable by a micrometer
until they straddle the
reflected image. There is a
scale in eyepiece which can
directly read to the nearest 1/2
minute. The micrometer drum
moves the setting wires at 1/2
minute per revolution and is
divided into 60 equal parts.
Thus with the aid of
Microptic Autocollimator
Fig. 8.37. Microptic Autocollimator.
micrometer it is possible to read the tilt of reflector to normal upto 1/2 sec. of arc. The two wires
help to indicate tilt of reflector in two planes at right angles.
The instrument has generally a range of readings of 10 minutes of arc upto distances of
9 metres. It is used for a variety of purposes.

Autocollimator Applications.

Autocollimators are applied to the measurement of
straightness and flatness; precise angular indexing in conjuction with polygons ; comparative
measurement using master angles ; assessment of squareness and parallelism of components
; and the measurement of small linear dimensions.
Straightness is measured in conjunction with a reflector attached to a base having two
co-planar locating pads at a known distance apart. The base is stepped in a straight line along
the surface at intervals equal to the pitch of the locating pads and the angular change is
recorded at each position. These readings are readily converted into changes in vertical height
of the leading pad. A plot of the surface straightness can then be prepared from the data.
Measurement of flatness is an extension of this method and involves a series of straightness
measurements along straight line axes across the surface.
Polygons provide precise angular references for testing rotary tables and angular
indexing systems. Supplied with a calibration of either ± 1 or ± 0.5 second of arc they can be
used to directly measure functional errors in the readouts of such equipment. Standard
polygons with 8,9 or 12 sides allow measurement at 45,40 and 30 degree intervals respectively.
Used in combination, the measurement interval is reduced to the difference between the
intervals of each polygon {e.g. a combination of 8 and 9-sided polygons allow measurement to
45 – 40 = 5 degrees). A great advantage of polygons is that they only require centering on the
table to about 250 |xm and levelling to 2 minutes of arc to give accuracies of + 1 second of arc
used singly and ± 2 seconds of arc used in combination.
Angular comparison can be achieved by simultaneous viewing of a component and a
master angle which can be either a combination of angle gauges or a master component. Two
images are produced in the autocollimator and their separation is a direct reading of angular
error. Squareness and parallelism measurements involve similar techniques of using reference
squares or viewing two reflectors simultaneously.
8.10.7. Calibration of Angle Gauges using Autocollimator. Angle gauge is wrung
on base platen. An optical flat is placed inclined at 02 to platen and Qt to angle gauge as shown
 Interferometric calibration of angle gauge.tmp4-56_thumb
Fig. 8.38. Interferometric calibration of angle gauge.
in Fig. 8.38. Two sets of fringes are observed. The fringes are counted over length L for gauge
and platen (say tii and n2). The angle of gauge 82 – ^i = “^ (“2 -
where X is the wavelength of the light used. The values of ni and rax in general will not be an
integral. This method can be used for angles upto 1 minute and the precision of 1 sec is possible.

Moire Technique Goniometers.

Fig. 8.39 shows in schematic form the working of Goniometer. It
incorporates continuously rotating Moire gratings for high accuracy angular measurements.
Two radial gratings rotating in unison are employed. These are scanned by two reading heads,
one remaining stationary and the
other moving with a rotatable
work table i.e. through the angle
to be measured. The phase dif-
ference between the two outputs
from heads varies continuously
as the second head attached to
the rotary table is moved and
provides an accurate measure of
the angle by which the work table
has been moved. The whole num-
ber of phase cycles is found by
counting, while the fraction is
measured with an accurate
This system has the ad-
vantage that grating errors are
almost entirely averaged to zero
during the measurement time
thus giving the instrument
inherent accuracy, even with
components manufactured with
relatively poor accuracy.
Schematic diagram of Moire technique for angle measurement.
Fig. 8.39. Schematic diagram of Moire technique
for angle measurement.
With an angle goniometer fitted with
two 32400 lines radial gratings, angle meas-
urements to an accuracy of 0.1 second of arc
are possible.

Angle Dekkor.

This is also a
type of an autocollimator. (Refer Fig. 8.40). It
contains a small illuminated scale in the focal
plane of the objective lens (collimating lens).
This scale in normal position is outside the
view of the microscope eyepiece as shown in
Fig. 8.41 (b). The illuminated scale is
projected as a parallel beam by the collimat-
ing lens which after striking a reflector below
the instrument is refocused by the lens in the
field of view of the eye-piece. In the field of
view of microscope there is another datum
scale [Fig. 8.41 (c)] fixed across the centre of
screen and the reflected image of the
illuminated scale is received at right angle to
this fixed scale as shown in Fig. 8.41 (a) and
 Angle dekkor
Fig. 8.40. Angle dekkor.
the two scales, in this position intersect each other. Thus the reading on the illuminated scale
measures angular deviations from one axis at 90° to the optical axis and the reading on the
fixed datum scale measures the deviation about an axis mutually perpendicular to the other
two. In other words, changes in angular position of the reflector in two planes are indicated by
changes in the point of intersection of the two scales. Readings from scale are read direct to 1′
without the use of a micrometer.
View in the eyepiece of angle dekkor.
Fig. 8.41. View in the eyepiece of angle dekkor.
The whole of the optical system shown in Fig. 8.40 is enclosed in a tube which is mounted
on an adjustable bracket. There is a lapped flat and reflective base on which all these things
are placed. It is mostly used as a comparator. The instrument measures by comparing the
readings obtained from a standard, a sine bar or combination of angle gauges with that from
the work under test. Though this is not a precise instrument in comparison to autocollimator,
it has wide field of application for general angular measurement, as angular variations are
read direct without the operation of a micrometer.

Uses of angle dekkor in combination with angle gauges.

(i) Measuring angle of a component. It may be made clear that angle dekkor is capable
of measuring small variations in angular setting, i.e. determining angular tilt. In operation
the measuring principle is that of measurement by comparison; the angle dekkor is set to give
a fixed reading from a known angle (i.e. using known angular standards to obtain a zero
reading). (Refer Fig. 8.43)
Thus first the angle gauge
combination is set up .to the
nearest known angle of the com-
ponent and the angle dekkor is
set, (using special attachment
and link), such that zero reading
is obtained on the illuminated
scale. The angle-gauge build up
is then removed and replaced by
the component under test, a
straight-edge being used to en-
sure that there is no change in
lateral positions. The new posi-
Zero-reading with angle gauge build-up
Zero-reading with angle gauge
Reading with component in position error = 40 - 20 = 20 divisions = 20 minutes
Reading with component in position
error = 40 – 20 = 20 divisions
= 20 minutes
Fig. 8.42
Measuring angle of a component.
Fig. 8.43. Measuring angle of a component.
tion of the reflected scale with respect to the fixed scale gives the angular tilt of the component
from the set angle. (Refer Fig. 8.42).
(ii) To obtain precise angular setting for machining operations. We will consider an
example of milling a slot at a precise angle to a previously machined datum face. A parallel
bar is used as a datum face, the component being securely clamped when in close contact with
 Set up for milling angular slot.
Fig. 8.44. Set up for milling angular slot.
it. The parallel bar is positioned on the table of milling machine with the aid of angle dekkor.
The setting-up technique is illustrated in Fig. 8.44. It may be noted that a polished reflector
is firmly attached to the column of the milling machine. With the aid of this surface as
reference, the angle dekkor is set up such that zero reading is obtained ; in other words, the
axis of the optical beam is truly at 90 to the table feed. Then build up the combination of angle
gauges to the exact value 0, i.e. the inclination of the slot to be milled on the component. The
angle gauges along with the parallel bar are placed on the table and adjusted in position such
that the angle dekkor shows zero reading when viewing the flat surface of the angle gauge
combination. It means that the angular inclination between the datum face of the parallel bar
and the feed direction of the table is now 9°. The parallel bar is firmly clamped in this position,
a check being made to ensure that no movement has taken place during clamping; a few gentle
taps will soon allow a zero reading on the angle dekkor to be regained. Finally, now the
workpiece can be clamped on milling machine table, in close contact with this pre-set parallel
(iii) Checking the sloping angle of a V-block. The set up for checking the sloping angle of
V-block is illustrated in Fig. 8.45 (a). The principle consists of comparing the reading obtained
from the polished slip gauge in close contact with the work-surface, and a zero reading obtained
from the angle-gauge build-up.
(a) Checking V-block angle. (b) Measuring angle of cone.
(a) Checking V-block angle. (b) Measuring angle of cone.
Fig. 8.45
(iv) To measure the angle of cone or taper gauge. A simple set-up for this purpose is shown
in Fig. 8.45 (b). The instrument is first set for the nominal angle of cone on a combination of
angle gauges or on a sine bar set to the nominal angle. The cone is then placed in position with
its base resting on the surface plate. A slip gauge or other parallel reflector is held against the
conical surface as no reflection can be obtained from a curved surface. Any deviation from the
set angle will be noted by the angle dekkor in its eye-piece and indicated by the shifting of
image of illuminated scale, whose reading while setting with angle gauge is noted down before
Angle dekkor and auto-collimator find a wide range of applications if used in conjunction
with the constant deviation prism and Dowell Prism. It is, therefore, considered better to
describe these prisms here.

Constant Deviation Prism.

This enables both the projected and reflected
beams to be turned through a right angle. It is, therefore, very suitable in alignment testing
and checking of two surfaces at right angles. This is also called optical square. The special
property of this prism is that it always reflects a ray of light through the same angle,
irrespective of the angle of incidence. In the prism, the reflecting surfaces are disposed at an
angle of 45°. As the ray is deflected through twice the angle between the reflectors, therefore,
it will be reflected through 90°. Actually the rays bend as they move from rare to dense medium
and similarly when coming out, but their effect is nullified and finally the beams are at right
angles. The effect of bending of rays is not shown in Fig. 8.46.
Optical Square.
Fig. 8.46. Optical Square.
Dowell Prism
Fig. 8.47. Dowell Prism.

Dowell Prism.

This is used to split up a beam of light into two beams which
are exactly parallel but projected in opposite directions. The special feature of the prism is that
its construction is such that the two projected beams are parallel under any conditions of light
transmission, thus no setting of prism or angle dekkor is required. This prism is very suitable
for testing the parallelism of two faces or surfaces. Since images from two surfaces will be seen
simultaneously in eye-piece, the error can be measured directly. In Fig. 8.47, AB and CD are
incident parallel rays and BG and EF are reflected parallel beams, but in opposite direction.

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