Scales and Gratings (Metrology)

6.11.
Scales are usually made of steel with lines (rulings) marked on them and spaced
relatively far apart, so that some sort of interpolating device like vernier device is required to
make accurate settings. In the case4>f gratings, the rules are so closely spaced as to produce aa
periodic pattern without blank gaps. It is impossible to make out anything with naked eye,
and therefore, special readout systems such as photo-electric type are required for this purpose.
Metal scales are usually made from stainless steel which has the advantages of taking
good finish, stability with time if properly treated, resistant to tranishing ; but has the
disadvantages of lower thermal coefficient of expansion than steel or cast iron. Depending on
the accuracy desired, the graduations on metallic scales may be produced by (i) cutting lines
with a V-section milling cutter on milling machine, (ii) etching through a ruled resist or a
photoetch resist copied from a glass master, or (Hi) engraving directly into the polished surface
with a sharp diamond.
Glass scales are also commonly used which can be easily polished, are stable, and are
able to work in both transmitted and reflected light. Though ordinary glass has 15—30 per
cent less thermal coefficient of expansion than steel, but glass scales, having same thermal
coefficient of expansion as steel, have been produced. The graduations on glass scales can be
produced (i) by etching through a ruled wax or photographic resist activated by contact or
projection printing, (ii) by depositing material in the form of very thin lines having very high
edge definition and highly resistant to wear, (Hi) by depositing photographic emulsion on glass.
Most of the scales are produced by duplicating from a master scale on ruling engine.
The master scale and the scale to be engraved are placed side by side, the master scale being
on a fixed table and the other on a carriage. The carriage is successively positioned until master
graduations are exactly in line with a reference in the form of a photoelectric microscope, and
lines marked on the scale.
Master scales are produced on ruling engines having an accurate lead screw (with
correction cams for errors), for successive indexing of the required interval. More sophisticated
machines use interferometer feedback control which measures the positioning errors against
the wavelength of a standard light source and takes corrective action till positioning error is
zero. Thus intervals can be divided to a great accuracy. All this work is done in rooms having
controlled atmosphere.
6.11.1. Readout Systems for Scales. Scales may be read by:
(i) naked eye, utilising vernier ;
(ii) aided by eye-piece or microscope ;
(Hi) projection systems which are finding more and more applications as these reduce
fatigue.
All scale readout systems utilise index mark, with reference to which scale reading is
noted. Three types of visual scale line setting against an index are possible and are illustrated
in Fig. 6.43. The type of index mark used plays a big role in the precision attainable. On
sophisticated machines, the last type finds much application due to high setting precision
available. It may be noted that in scales, the sharply defined edges are more critical and not
the line widths.
Types of visual scale line setting against an Index mark
Fig. 6.43. Types of visual scale line setting against an Index mark.
Two types of projection systems commonly used are :
(i) Index mark is moved mechanically until it frames the scale line, and the amount of
movement required is read optically on the same screen, or externally.
(ii) Index line is kept fixed, and the image of the scale is moved with a suitable optical
device such as a sliding lens or tilting glass plate, and the required motion to achieve settings
are displayed optically on the screen.
The description of an optical projection system to read scale, employed in a universal
length measuring machine is given below: (This description is based on literature ofVEB Carl
Zeiss JENA.)
Measuring Principle
In this machine, measurements are based upon direct comparison of the test specimen
with built-in precision glass scales. The standard is made up of a number of aligned steel bars,
which carry glass index marks at distances of 100 mm each. It combines the advantages of
steel scales, i.e. the same coefficient of expansion as instrument and test piece, with the merits
of glass scales, viz. excellent divisibility and parallax-free observation in transmitted light. As
there is no graduation between the glass index marks on the steel bars, the intermediate values
may be read in the microscope of the measuring carriage. Both the index glass marked and
the graduation of the measuring carriage are imaged at a magnification of 75 x in the image
plane of the microscope together with an index line by means of a special arrangement of three
optically associated collimators. This arrangement compensates for any existing deviations in
the guideways of the bed. The scales are located in the single focal length of the objective, and
the measuring axis in the double focal length.
Description
A rugged bed carries the scale, the measuring unit and the test specimens. Measuring
unit and holding devices for test specimens slide on two different guideways. This enables the
measuring unit to be moved along the entire length of the test specimen and to take
measurements at any optical plane of the latter. This arrangement also means that the
guideways for the measuring carriage and for the scale are protected against premature wear.
They are no longer overloaded by heavy test piece and cannot be damaged by awkward
application of these test specimens.
The scale is rigidly connected to the bed over its entire length thus ensuring that any
slight distortion that may occur, will not influence the measurement.
Tightly screwed down to the front guideway is the headstock with spindle, which is
provided with a condenser for illuminating an index mark inserted into the steel scale and
with a collimator lens which depicts the index.
Likewise attached to the front guideway of the bed is the two-element measuring
carriage (lower and upper carriage). The lower one carries the reading microscope, with the
aid of which readings down to 1 micron may be taken; tenths of a micron being easily estimated.
The upper carriage, which may be displaced relative to the lower one, can be provided with
various measuring devices or with the measuring microscope.
A decimeter graduation at the front guideway of the measuring element enables the
upper carriage to be roughly oriented relative to the lower one. With the aid of a clamp the
lower carriage may be rigidly connected with the bed, the upper and lower carriage may also
be interconnected by clamps. A slow motion drive permits of an exact setting of the lower
carriage to the decimetre lines of the scale; with a second slow-motion drive, orientation of the
upper carriage relative to the test piece will be possible.
Mounted between clamping device and fine-setting of the upper carriage are spring
contacts, which cause a green pilot lamp to light up, as soon as the upper carriage is pressed
against the test piece (by moving the lower carriage) with a measuring pressure of about 300
g. When exceeding this pressure a red pilot lamp will light up.
Path of Rays. Refer Fig. 6.44.
The reading optics of the scales reposes on three different systems.
The optics of the first system, shown with less dense, dots, e.g. L1; Kx, Bj MD, Fx, M0,
Mi, Mg,M3, M3, M4) Me, M6, is rigidly connected with the bed.
The optics of the second one (not marked by any dots) represents a definite part of the
measuring equipment, which is fixed to the lower carriage and may be moved over the entire
length of the three metre bed.
The third system, marked in more dense e.g. L2, K2, B2, F3, is a fixed part of the upper
carriage onto which all measuring or aligning units may be clamped. Its range of movement
on the lower carriage is 100 mm.
Optics in universal length measuring machine
Fig. 6.44. Optics in universal length measuring machine.
By way of condenser Ki, the light of lamp Li of the headstock illuminates the double
index mark MD which is imaged at infinity by the objective Fi„ Passing through the beam
splitting cube Ti, the beams arrive at objective F2 and (depending on the position of the lower
carriage on the bed) are then imaged in the image plane of the measuring mark Mo upto M2g
via beam-splitting cube T2. In Fig. 6.45, the reading of microscope is set to measuring mark
M5. By looking into reading microscope AM, both image (MD and M5) are set by the operator
in such a way that double index markMD symmetrically brackets the line of measuring mark
M5. This setting guarantees a constant, well-adjusted distance between scale Mst and the
respective measuring marks Mj upto M29.
Via condenser K2, the light L2 is directed to the tenth-millimetre scale Mst which is
imaged at infinity by objective F3. Furthermore, the rays passing through measuring wedges
MK, prism Px and beam splitting cube Tx, arrive at objective^, which images scale Mst in the
plane of measuring markM5.
The light of lamp L3, conducted to fluorescent mark LM by condenser K3 is directed to
objective F4 via beam-splitting cube T3, causing the flourescent mark to be imaged at infinity.
By way of prisms, the light beams are conducted to objective F5, which through beam-splitting
cube T2, images fluorescent mark LM in the plane of measuring mark M5. Both, the image of
fluorescent mark LM and of scale Mst are brought to coincidence with the aid of the microscope
by displacing the image of the scale while turning measuring wedges MK. Micrometer scale
MT is connected with measuring wedges MK, thus permitting the rotation of the measuring
wedges to be read in microns. Illumination of micrometer
scale MT is effected by filament lamp via condenser K4, from
where it is directed through beam-splitting cube T3 to objec-
tive F4.
It is likewise by way of prism that micrometer scale
MT is directed to objective F5, from where it is imaged
through beam splitting cube T2 in the plane of measuring
mark M5. This mark is viewed with the same reading
microscope AM as used in the aforementioned paths of rays.
Situated directly behind condensers Klt K2 and K4 are
diaphragms Bx to B3. They ave intended to prevent irradia-
tions in the three-partite field of vision of reading micro-
scope AM. All scales and measuring marks (MD, M5 Mst,
MT) are to be seen in one microscope (AM) and the measur-
ing values may be taken at once (also refer Fig. 6.45).
Reading the measured value
Reading the scale
Fig. 6.45. Reading the scale.
The lower carriage of the measuring equipment is clamped in such a position that its
index is in line with the decimeter mark on the metal scale. As soon as the scale line is
symmetrically bracketed between the double index mark, the decimetre values are read in the
upper scale of the visual field. Having done this, one scale division of the 100 mm scale is to
be set symmetrically to the fluorescent thick line (to be seen in Fig. 6.45 as a dotted field) by
optical deflection. The value thus received (96.5 in this case) represents the full millimetre and
the tenths of a millimetre. Readings of the hundredths and thousandths of a millimetre are
taken at the lower scale, ten thousandths may be estimated. (0.0794 mm in Fig. 6.45).
Total reading:
2400 reading of the higher scale
96.5 reading of the middle scale
0.079 (4) reading of the lower scale
2496.579 (4) mm
The optical schematic of another direct-
reading optical gauge is shown in Fig. 6.46 in
which the main scale is integral with the measur-
ing spindle, and its graduations are imaged on
two vernier scales and then both are projected
superimposed on viewing screen. The zeroing
glass has two lines engraved in it and serves a
datum. The vernier scale can be slided in
transverse direction and contains a line which
moves up or down along incline to provide setting.
For any reading, the vernier is so set that the
horizontal line in it comes exactly in the centre of
two index lines of zeroing glass. Then the reading
can be noted from the image at ground glass screen.
In yet another system providing digital in-line scale readout (Fig. 6.47), the scale is
imaged by means of relay lenses through dove prism onto plane of vernier scale which can be
moved up and down by a knob. Combined image of main scale and vernier scale is projected
by lens L onto a screen and viewed through the magnifier. To take reading, vernier slide with
lens is moved until scale line is symmetric with index lines.
. Optical schematic of direct reading optical gauge.
Fig. 6.46. Optical schematic of direct reading
optical gauge.
6.11.2. Gratings in Metrology. Gratings have brought about a great revolution in the
methods of measurement. The visual readings of scales, micrometers, and measuring micro-
scopes have been largely replaced by the use of transducers producing electrical signals
suitable for operating counters, display units and servo devices.
Metrological transmission gratings consist of a regular succession of opaque lines
separated by clear spaces of equal width. If a slit of width equal to one grating line is placed
parallel to lines of grating and moved perpendicular to lines of grating over this grating, and
Digital in-line scale readout device
Fig. 6.47. Digital in-line scale readout device.
a photocell is placed at bottom of grating and the grating be illuminated by a normal incident
light, then the photo-cell output will rise to a maximum when slit is exactly over the line and
fall to zero when slit is exactly over the gap. One such cycle of maximum brightness and
darkness sensed by the photocell is a measure of the traverse of one grating period. It is very
interesting to note that if this slit be replaced by a short length of index grating exactly similar
to the main grating, then output of photocell shall firstly be increased due to light passing
through a multiple arrays of slits and secondly, the more important aspect, any local or periodic
irregularities on any of the two gratings shall be averaged out or improved due to averaging
effect of the multiple slits. In this way a measurement is made which is more accurate than
the grating itself. This principle is utilised in manufacture of grating and not in measurement.
Moire Fringes. Moire is the name given to the patterns formed by the overlapping of two
layers of fine fabrics. Moire fringes are observed when the index grating, instead of being kept
parallel to the scale grating, is rotated slightly in its own plane. Under such condition, the lines
of the two gratings intersect and the intersections are clearly visible as dark moire fringes
running approximately at right angles to the grating lines. If the index grating is moved
transversely, then the moire fringes move up or down and the position of the fringes repeats
itself every time the grating has moved one grating period.
In fact when the index grating having same spacing as scale grating is moved transver-
sely, then the fringes bisect at obtuse angle between the two gratings. Reading heads are used
to measure the movement of the moire fringes. Various types of reading heads are :
(i) Spectroscopic, (ii) Normal incidence,
(iii) Mirror image, (iv) Phase modulated.
6.11.3. Formation Of Moire’ fringes. A metrological grating is a scale having a large
number of equally spaced parallel lines. If two transparent gratings are put one over the other
with their ruled surface as close together as possible and their ruling crossing at a small angle,
a pattern of dark lines and fringes is formed
in a direction perpendicular to that of the
rulings, when the grating is observed against
a uniformly illuminated background (Fig.
6.48). These fringes are called ‘Moire’,
‘fringes’. The distance between successive
moire’ fringes is large as compared to the line
spacing of the scale, if the angle of inclination
of the two sets of lines is small. By keeping
one of the grating at rest and moving the
other slowly, the fringes are also found to
move at a magnified rate. Thus a relatively
coarse measurement of fringe displacement
can give an accurate measure of the actual
movement. The magnification is equal to the
ratio of the distance between adjacent Moire’
fnnges(s) and the distance between adjacent lines on the grating (p0). This method does not
depend in any way on the wave nature of light. The distance between Moire fringes being much
larger in comparison to spacings of grating, these can be easily counted by photocell.
Fig. 6.48 demonstrates the formation of a Moire’ pattern of this type. Let the line
separation or pitch of the specimen grating be pi and the reference grating pitch bep0, then it
can be shown by geometry that the perpendicular spacing of the fringes resulting from the
superimposition of the two is
The formation of Moire' fringes.
Fig. 6.48. The formation of Moire’ fringes.
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