Principle of InterferometryPrinciple of Interferometry

When light rays from a monochromatic source When light rays from a monochromatic source travel in different path lengths and travel in different path lengths and recombine, they will have a phase difference.recombine, they will have a phase difference.

The resultant light will have maximum The resultant light will have maximum intensity at an instant when the constituent intensity at an instant when the constituent rays are in phase, and minimum intensity (or rays are in phase, and minimum intensity (or zero) when they are out of phase.zero) when they are out of phase.

These effects are called “Interference” & the These effects are called “Interference” & the study is called “Interferometry”.study is called “Interferometry”.

Waves in phase & out of phaseWaves in phase & out of phase

Waves in phase Waves out of phase

Resultant wave Resultant wave

Method of producing Interference bandsMethod of producing Interference bands

O

P

M

N

Q

(Bright)

(Dark)

(Bright)

(Bright)

(Dark)

Slit A

Slit C

Slit B

Light Source

Method of producing Interference bandsMethod of producing Interference bands

As shown in the fig, light passes through a very As shown in the fig, light passes through a very narrow slit ‘A’ & then through the slits ‘B’ & ‘C’ narrow slit ‘A’ & then through the slits ‘B’ & ‘C’ which are close to each other.which are close to each other.

Thus, two separate beams of light are formed Thus, two separate beams of light are formed which will further travel towards a screen.which will further travel towards a screen.

At a point ‘O’ where the rays travel equal At a point ‘O’ where the rays travel equal distances, and hence will be in phase, a bright distances, and hence will be in phase, a bright band is produced.band is produced.

At a point ‘M’ where the path difference will be At a point ‘M’ where the path difference will be equal to one half the wavelength, i.e. equal to one half the wavelength, i.e. the the waves will be 180waves will be 180o o out of phase, resulting in a dark out of phase, resulting in a dark band.band.

Method of producing Interference bandsMethod of producing Interference bands

Similarly at a point ‘P’ where the path Similarly at a point ‘P’ where the path difference is one wavelength, the waves will difference is one wavelength, the waves will be again in phase and result in a bright be again in phase and result in a bright band.band.Thus, if the path difference is an Thus, if the path difference is an ‘even ‘even multiple of half wavelengths’multiple of half wavelengths’ the light waves the light waves will be in phase resulting in bright spots on will be in phase resulting in bright spots on the screen.the screen.If the path difference is an If the path difference is an ‘odd multiple of ‘odd multiple of half wavelengths’half wavelengths’ the light waves will be out the light waves will be out of phase resulting in dark spots on the of phase resulting in dark spots on the screen.screen.

Optical FlatsOptical Flats

Optical FlatsOptical FlatsAn optical flat is a circular piece of unstressed An optical flat is a circular piece of unstressed glass or quartz usually about 5 cm or more. (High glass or quartz usually about 5 cm or more. (High quality optical quartz or borosilicate glass is quality optical quartz or borosilicate glass is commonly used)commonly used)

The upper & lower surfaces are ground optically The upper & lower surfaces are ground optically flat to get reference planes.flat to get reference planes.

The flats will be coated with a thin film of titanium The flats will be coated with a thin film of titanium oxide to reduce the light lost by reflection.oxide to reduce the light lost by reflection.

Type ‘A’ optical flats have only one flat surface Type ‘A’ optical flats have only one flat surface while type ‘B’ has two parallel flat surfaces.while type ‘B’ has two parallel flat surfaces.

Cleanliness is utmost important as dust will result Cleanliness is utmost important as dust will result in inaccurate measurement. Also optical flats get in inaccurate measurement. Also optical flats get rapidly heated by handling & takes long time to rapidly heated by handling & takes long time to regain ambient temperature.regain ambient temperature.

Principle of Operation of Optical flatsPrinciple of Operation of Optical flats

(Interferometry applied to flatness testing(Interferometry applied to flatness testing))

A

B

D

F

E

C

K

HL

MJ

In phase

out of phaseDark band

Optical flat

Surface tested

G

Principle of Operation of Optical flatsPrinciple of Operation of Optical flats

When an optical flat is put into close contact with a When an optical flat is put into close contact with a surface to be tested, it will produce interference surface to be tested, it will produce interference fringes, which indicates the contour of the surface.fringes, which indicates the contour of the surface.

A ray of light entering at A ray of light entering at AA is partly reflected at is partly reflected at BB along BC and partly transmitted to be reflected at along BC and partly transmitted to be reflected at DD along DEF.along DEF.

The difference in lengths of paths is (BD+DE) and if The difference in lengths of paths is (BD+DE) and if this is an even multiple of half wavelength of incident this is an even multiple of half wavelength of incident light, a bright band will be seen.light, a bright band will be seen.

If at another position If at another position G, G, if theif the path differencepath difference (HK+KL) is an odd multiple of (HK+KL) is an odd multiple of a dark band will a dark band will result.result.

Principle of Operation of Optical flatsPrinciple of Operation of Optical flats

If the test surface is perfectly wrung together with If the test surface is perfectly wrung together with optical flat, then no air gap exists & hence no optical flat, then no air gap exists & hence no interference fringes will be observed.interference fringes will be observed.

If the surface is nearly flat, If the surface is nearly flat, widely spacedwidely spaced parallel parallel fringes will appear.fringes will appear.

If the angle If the angle air wedge between test surface & air wedge between test surface & optical flat) is increased, the pitch of the fringes optical flat) is increased, the pitch of the fringes become small. become small.

The fringe pattern observed indicate the nature of The fringe pattern observed indicate the nature of test surface. Some typical fringe patterns are test surface. Some typical fringe patterns are shown in fig which indicate the contour of the test shown in fig which indicate the contour of the test surface.surface.

Pattern of fringes for different contoursPattern of fringes for different contours

convex

concave

optical flat

surface

Fringe pattern

convex

(a)

(b)

(c)

(d)

Pattern of fringes for different contoursPattern of fringes for different contours

convexconcave

(e)

(f)

(g)

Pattern of fringes for different contoursPattern of fringes for different contoursPattern (a) & (b) represent flat surfaces. Pattern (a) & (b) represent flat surfaces. The inclination of optical flat is more in The inclination of optical flat is more in case (b) than case (a).case (b) than case (a).Fig (c) represents spherical surface. Figs Fig (c) represents spherical surface. Figs (d) & (e) indicate concave & convex (d) & (e) indicate concave & convex surfaces which is decided by pressing the surfaces which is decided by pressing the flat slightly at the centre & the edges.flat slightly at the centre & the edges.Fig (f) is the fringe pattern obtained for a Fig (f) is the fringe pattern obtained for a smooth cylindrical surface.smooth cylindrical surface.Fig (g) represents the pattern over a V-Fig (g) represents the pattern over a V-block.block.

AutocollimatorAutocollimatorAutocollimator is an optical device used for Autocollimator is an optical device used for measurement of small angular differences measurement of small angular differences accurately. It is essentially an ‘accurately. It is essentially an ‘infinity telescope’ infinity telescope’ and aand a ‘collimator’ ‘collimator’ combined into one instrument.combined into one instrument.A source of light ‘A source of light ‘O’O’ is placed at the focal plane of is placed at the focal plane of a collimating lens. The light rays from O incident a collimating lens. The light rays from O incident on the lens will travel as parallel beam & strike a on the lens will travel as parallel beam & strike a plane reflector which is normal to its optic axis.plane reflector which is normal to its optic axis.The reflected rays travel back along the same path The reflected rays travel back along the same path and get refocused at the same point O.and get refocused at the same point O.If the plane reflector is tilted through a small angle If the plane reflector is tilted through a small angle then the parallel beam gets deflected through 2 then the parallel beam gets deflected through 2 and will be refocused at and will be refocused at O’, O’, such that such that OO’=x= OO’=x= 2 2 f, f, where where f f is the focal length of the lens.is the focal length of the lens.

Principle of reflectionPrinciple of reflection

X

Point source

O

O'

Focal plane Collimating lensPlane reflector

Principle of reflection

Principle of Microptic AutocollimatorPrinciple of Microptic Autocollimator

f

Lamp

Eye piece Measuringgraticule

diffuser

Cross line (target) graticule

Beam splitterobjective lens

Reflectoron workpiece

Principle of Microptic AutocollimatorPrinciple of Microptic AutocollimatorA cross line A cross line target graticuletarget graticule is positioned at the is positioned at the focal plane of a telescope’s objective system.focal plane of a telescope’s objective system.

When the target graticule is illuminated, rays of When the target graticule is illuminated, rays of light reach the objective lens via a beam splitter & light reach the objective lens via a beam splitter & then move towards the reflector as a parallel beam then move towards the reflector as a parallel beam of light. In this mode, the system operates as a of light. In this mode, the system operates as a “Collimator”.“Collimator”.

The flat reflector reflects the light back along their The flat reflector reflects the light back along their original paths. A portion of this light passes original paths. A portion of this light passes straight through the beam splitter and image of straight through the beam splitter and image of target cross line is visible through the eye piece. In target cross line is visible through the eye piece. In this mode the system operates as a ‘telescope this mode the system operates as a ‘telescope focused at infinity’.focused at infinity’.

Principle of Microptic AutocollimatorPrinciple of Microptic Autocollimator

If the reflector is tilted through a small angle, If the reflector is tilted through a small angle, then the reflected beam of light will be then the reflected beam of light will be deflected by twice the angle of tilt and will be deflected by twice the angle of tilt and will be brought to focus in the plane of the target brought to focus in the plane of the target graticule but linearly displaced from actual graticule but linearly displaced from actual target cross lines by an amount 2target cross lines by an amount 2f.f.

Linear displacement of the graticule image Linear displacement of the graticule image is directly measured by an eyepiece or is directly measured by an eyepiece or optical micrometer.optical micrometer.

The focal length determines the sensitivity & The focal length determines the sensitivity & the angular measuring range.the angular measuring range.

Autocollimator models

AutocollimatorAutocollimator

Screw ThreadsScrew ThreadsScrew threads are used;Screw threads are used;

To hold parts together (ex: V-threads)To hold parts together (ex: V-threads)

To transmit motion & power (To transmit motion & power (Square, Acme threads)Square, Acme threads)

Screw threads TerminologyScrew threads TerminologyPITCHPITCH:: The distance from a point on a screw The distance from a point on a screw thread to a corresponding point on the next thread thread to a corresponding point on the next thread measured parallel to the axis. measured parallel to the axis.

LEADLEAD: The distance a screw thread advances in : The distance a screw thread advances in one turn. For a single start threads, lead=pitch,one turn. For a single start threads, lead=pitch,

For double start, lead=2xpitch, & so on.For double start, lead=2xpitch, & so on.

THREAD FORMTHREAD FORM: The cross section of thread cut : The cross section of thread cut by a plane containing the axis.by a plane containing the axis.

MAJOR DIAMETER: MAJOR DIAMETER: This is the diameter of an This is the diameter of an imaginary cylinder, co-axial with the screw, which imaginary cylinder, co-axial with the screw, which just touches the crests of just touches the crests of an external thread or an external thread or roots of an internal threads. It is also called as roots of an internal threads. It is also called as ‘Nominal diameter’.‘Nominal diameter’.

Pitch Crest

Root

Flank

ThreadAngle

Pitch line

Axis of thread

Axial thickness

Addendum

Dedendum

Flankangle

Major dia Pitch dia Minor dia

EXTERNAL THREAD TERMINOLOGY

SCREW THREAD TEMINOLOGY

Screw threads TerminologyScrew threads TerminologyMinor diameterMinor diameter: This is the diameter of an imaginary : This is the diameter of an imaginary cylinder, co-axial with the screw which just touches the cylinder, co-axial with the screw which just touches the roots of an external thread or the crest of an internal roots of an external thread or the crest of an internal thread. This is also referred to as ‘thread. This is also referred to as ‘rootroot’ or ‘’ or ‘corecore diameterdiameter’.’.

Effective diameterEffective diameter or or Pitch diameterPitch diameter: It is the diameter : It is the diameter of an imaginary cylinder coaxial with the axis of the of an imaginary cylinder coaxial with the axis of the thread and intersects the flanks of the thread such that thread and intersects the flanks of the thread such that width of the threads & width of spaces between width of the threads & width of spaces between threads are equal.threads are equal.

FlankFlank: It is the Thread surface that connects crest with : It is the Thread surface that connects crest with root.root.

Depth of threadDepth of thread: It is the distance between crest and : It is the distance between crest and root measured perpendicular to axis of screw.root measured perpendicular to axis of screw.

Screw threads TerminologyScrew threads TerminologyAngle of threadAngle of thread: Included angle between sides of : Included angle between sides of thread measured in axial plane.thread measured in axial plane.

Helix angleHelix angle: Angle that thread makes with plane : Angle that thread makes with plane perpendicular to thread axis.perpendicular to thread axis.

Flank angle: Flank angle: It is half the included angle of the It is half the included angle of the thread.thread.

Addendum: Addendum: It is the distance between the crest It is the distance between the crest and the pitch line measured perpendicular to axis and the pitch line measured perpendicular to axis of the screw.of the screw.

Dedendum: Dedendum: It is the distance between the pitch It is the distance between the pitch line & the root measured perpendicular to axis of line & the root measured perpendicular to axis of the screw.the screw.

Errors in screw threadsErrors in screw threads

There are six important elements in a thread, There are six important elements in a thread, errors in any one of which may lead to rejection.errors in any one of which may lead to rejection.

They are Major dia, Minor dia, effective dia, Pitch, They are Major dia, Minor dia, effective dia, Pitch, Flank angle and the profile at root & crest.Flank angle and the profile at root & crest.

Errors in screw threads may cause interference Errors in screw threads may cause interference with mating threads or slackness due to improper with mating threads or slackness due to improper flank contact.flank contact.

Errors in pitch of screw thread may be classified Errors in pitch of screw thread may be classified into three types;into three types;

(i) Periodic errors (ii) Progressive errors (iii) Erratic (i) Periodic errors (ii) Progressive errors (iii) Erratic errorserrors

(i) Periodic errors(i) Periodic errorsPeriodic errors are those which vary in magnitude Periodic errors are those which vary in magnitude along the length of the thread and occurs at along the length of the thread and occurs at regular intervals as shown in fig (a). regular intervals as shown in fig (a).

A ‘A ‘drunken thread’drunken thread’ is a particular case of periodic is a particular case of periodic error where the error repeats once per turn.error where the error repeats once per turn.

For a For a true threadtrue thread, if the thread is imagined to be , if the thread is imagined to be unwound from the pitch cylinder, the helix will be a unwound from the pitch cylinder, the helix will be a straight line. For a straight line. For a drunken threaddrunken thread, it will be a , it will be a curve as shown in fig (b).curve as shown in fig (b).

In a drunken thread, the advance of the helix is In a drunken thread, the advance of the helix is irregular in one complete revolution. This is due to irregular in one complete revolution. This is due to thread being not cut to true helix.thread being not cut to true helix.

(i) Periodic errors(i) Periodic errors

+

_

Cum

ulat

ive

pitc

h er

ror

Length of thread

Fig (b)

PERIODIC ERRORS

Mean diameter

Pitc

h

Max error

True thread

Drunkenthread

DRUNKEN THREAD

Fig (a)

Progressive pitch errorProgressive pitch error: : If the pitch of the If the pitch of the thread is uniform but is longer or shorter thread is uniform but is longer or shorter than its nominal value, then the error is than its nominal value, then the error is called progressive as shown in fig (c). called progressive as shown in fig (c). These errors may be caused by a change in These errors may be caused by a change in length due to hardening, or by the errors in length due to hardening, or by the errors in the pitch of the lead screw, or by the faults the pitch of the lead screw, or by the faults in the saddle guide ways.in the saddle guide ways.Erratic errorsErratic errors: : These errors vary in irregular These errors vary in irregular manner along the length of the thread as manner along the length of the thread as shown in fig (d). Their causes are difficult to shown in fig (d). Their causes are difficult to identify. Possible sources are faults in the identify. Possible sources are faults in the machine and irregular cutting action machine and irregular cutting action resulting from material non uniformity.resulting from material non uniformity.

(ii) Progressive & (iii) Erratic errors(ii) Progressive & (iii) Erratic errors

Length of thread

Cum

ulat

ive

pitc

h er

ror

Length of thread

Cum

ulat

ive

pitc

h er

ror

ERRATIC ERRORSPROGRESSIVE ERRORFig (c) Fig (d)

Measurement of major diameterMeasurement of major diameterClamp

FiducialIndicator

MeasuringAnvils Holding centres

Micrometer head

Supports

BENCH MICROMETER

Bench Micrometer

BENCH MICROMETER

Bench MicrometerBench MicrometerA good quality hand held micrometer is quite suitable for A good quality hand held micrometer is quite suitable for measuring external thread, but only light pressure has to measuring external thread, but only light pressure has to be applied on the anvils to make only contact on the screw be applied on the anvils to make only contact on the screw threads.threads.Excessive pressure may lead to elastic deformation of Excessive pressure may lead to elastic deformation of screw threads leading to errors.screw threads leading to errors.A A bench micrometerbench micrometer may be used for greater accuracy may be used for greater accuracy which give direct readings of 0.0002 mm.which give direct readings of 0.0002 mm.A standard cylinder of known diameter A standard cylinder of known diameter ‘S’‘S’ (which is nearly (which is nearly equal to thread diameter) is held between centers & a equal to thread diameter) is held between centers & a reading Rreading R11 between the fiducial indicator anvil & between the fiducial indicator anvil & micrometer anvil is taken. The cylinder is then removed.micrometer anvil is taken. The cylinder is then removed.Then the screw thread to be measured is held between Then the screw thread to be measured is held between centers & a second micrometer reading Rcenters & a second micrometer reading R2 2 is taken. is taken.

Then DThen D11 =S(+ or -) (R =S(+ or -) (R11~R~R22))

Holding centre

Measuring anvil

Holding centre

Measuring anvil

Stan

dard

Cyl

inde

r

Scre

w T

hrea

d

Measurement of Major diameter

MeasurementMeasurement of minor diameterof minor diameterThe principle of minor diameter is same as The principle of minor diameter is same as that of measuring major diameter except that of measuring major diameter except that that v -shaped prismsv -shaped prisms are used. are used.Prisms of suitable sizes are placed between Prisms of suitable sizes are placed between the standard cylinder and the instrument the standard cylinder and the instrument anvils in order to take a reading first anvils in order to take a reading first micrometer reading Rmicrometer reading R11..

The standard cylinder is then replaced by The standard cylinder is then replaced by the screw thread and a second reading Rthe screw thread and a second reading R22 is is taken as shown in fig.taken as shown in fig.

Then the minor diameter DThen the minor diameter D22=S +(or -)=S +(or -)(R(R11~R~R22))

Holding centre

Fiducialindicator anvil

Stan

dard

Cyl

inde

r

Scre

w T

hrea

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Measurement of Minor diameter

Prism

PrismMicrometer anvil

SR1

R2

Measurement of Flank angleMeasurement of Flank angle

10

20

0 10

20

Shadow Protractor

Screw Pivot

Protractor arm

Protractor

Shadow protractorShadow protractorShadow protractor is most convenient method for Shadow protractor is most convenient method for measurement of flank angles using optical projection.measurement of flank angles using optical projection.The shadow of the thread is viewed on a screen and the The shadow of the thread is viewed on a screen and the angles are measured by means of a protractor.angles are measured by means of a protractor.For clear definition of a thread form on the screen it is For clear definition of a thread form on the screen it is necessary to project the light beam along the thread helix necessary to project the light beam along the thread helix angle by using a lamp & collimating unit.angle by using a lamp & collimating unit.The protractor is supported at the screen on a straight edge. The protractor is supported at the screen on a straight edge. The pivoted arm of the protractor is rotated until its shadow is The pivoted arm of the protractor is rotated until its shadow is parallel to the flank & the first reading is taken.parallel to the flank & the first reading is taken.The screw is then rotated 90The screw is then rotated 90oo to its axis and the protractor is to its axis and the protractor is swung about its pivot and adjusted to measure the angle of swung about its pivot and adjusted to measure the angle of the same flank and a second reading is taken.the same flank and a second reading is taken.The mean of the two readings is then the angle between the The mean of the two readings is then the angle between the flank & normal to the screw axis.flank & normal to the screw axis.

Measurement of Measurement of effectiveeffective diameter by Two wire method diameter by Two wire method

E M

B C

P

E

M

Dia 'd'

D EF

MEASUREMENT BY TWO WIRE METHOD

Pitch lineC

G

Measurement of effective diameter using two wire methodMeasurement of effective diameter using two wire method

The effective diameter can not be measured directly The effective diameter can not be measured directly but can be calculated from the measurements made.but can be calculated from the measurements made.Wires of exactly known diameters are chosen such Wires of exactly known diameters are chosen such that they contact the flanks at their straight portions.that they contact the flanks at their straight portions.

If the size of the wire is such it contacts the flanks at If the size of the wire is such it contacts the flanks at the pitch line, it is called the ‘the pitch line, it is called the ‘best size’ best size’ of wire which of wire which can be determined by geometry of screw thread.can be determined by geometry of screw thread.The screw thread is mounted between the centers & The screw thread is mounted between the centers & wires are placed in the grooves and reading M is wires are placed in the grooves and reading M is taken.taken.Then the effective diameter E =T+CThen the effective diameter E =T+Cwhere T =M-2d, & C is a value which depends on where T =M-2d, & C is a value which depends on diameter of wire, pitch & angle of the screw thread.diameter of wire, pitch & angle of the screw thread.

Measurement of effective diameter using two wire methodMeasurement of effective diameter using two wire method

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Effective diameter by three wire methodEffective diameter by three wire method

E M

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Effective diameter by three wire methodEffective diameter by three wire method

This method is more accurate than two wire This method is more accurate than two wire method as it ensures alignment of micrometer method as it ensures alignment of micrometer faces parallel to the thread axis.faces parallel to the thread axis.

Here, three wires of exactly known diameters Here, three wires of exactly known diameters are used, one on one side & the two on the other are used, one on one side & the two on the other side. The wires may be held in hand or hung side. The wires may be held in hand or hung from a stand.from a stand.

From the fig, M=diameter over the wiresFrom the fig, M=diameter over the wires

E= effective diameter (to be found)E= effective diameter (to be found)

d= diameter of wires, h=height of wire center d= diameter of wires, h=height of wire center above the pitch line, r=radius of wire, H=depth of above the pitch line, r=radius of wire, H=depth of thread, D=major diameter of the thread.thread, D=major diameter of the thread.

Effective diameter by three wire methodEffective diameter by three wire method

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Pitch Measuring machinePitch Measuring machine

Base

Fiducialindicator

Pointer T

Spring loaded head

stylus

Micrometer

Carriage

centers Screw thread

Pointer K

Pitch Measuring machinePitch Measuring machine

For measuring pitch, two methods are commonly For measuring pitch, two methods are commonly employed as follows;employed as follows;

(a) Using pitch measuring machine(a) Using pitch measuring machine

(b) Using Toolmaker’s microscope(b) Using Toolmaker’s microscope

In a In a pitch measuring machinepitch measuring machine, the screw , the screw thread is mounted between the centers of the thread is mounted between the centers of the machine. A stylus inserted into a spring loaded machine. A stylus inserted into a spring loaded head makes contact at the thread flanks near head makes contact at the thread flanks near the pitch line.the pitch line.

The stylus is positioned by and an initmoved The stylus is positioned by and an initmoved parallel to the axisparallel to the axis

Tool maker’s microscopeTool maker’s microscope

Lamp

Hollow base

Collimator lens

Base

Column

Eye pieceOptical head

Mirror

work tablewith carriage

TOOLMAKER’STOOLMAKER’S MICROSCOPE MICROSCOPE

TOOLMAKER’STOOLMAKER’S MICROSCOPE MICROSCOPE

GEAR TOOTH CALIPERGEAR TOOTH CALIPER

GEAR TESTERGEAR TESTER

GEAR TOOTH NOMENCLATUREGEAR TOOTH NOMENCLATURE

E M

Anvil

Wire

Screw thread

P

C

A

D FG

MEASUREMENT OF EFFECTIVE DIAMETER BY TWO WIRE METHOD

M