The following article is a translation of parts of the original

publication of Karl-Ludwig Bath in the german astronomical

magazine:

“Sterne und Weltraum 1973/6, p.177-180”.

The publication of this translation on the interferometer wiki

(http://starryridge.com/mediawiki-1.9.1) is with kind permission

of the author and the copyright holders of the original article at

Sterne und Weltraum, represented by Uwe Reichert, SuW

Heidelberg, Germany. Translation by Andreas Derwahl.

fig. 1: schematic representation of the interferometer, working principle see text, R is the autocollimation focus.

KARL-LUDWIG BATH

A simple interferometer for testing astronomical optics

Fellow stargazers have access to

a whole range of qualitative and

quantitative methods for the

analysis of astronomical optics.

[1]. There are different reasons,

however, that interferometric

methods are virtually non existent

among amateur telescope

makers. The following pages

describe an interferometer that

can be easily assembled and

adjusted with little practice, but

still gives accurate quantitative

results and is made from parts

that can be found in every cheap

binoculars.

To sum up a few of the specifics:

- The interferometer is suitable

for all usual f-ratios and focal

lengths down to about 25 cm.

- It can be used with white,

unpolarized light.

- The interferometer yields

bright interferograms. When

using a laser the efficiency at

exit port A2 (see fig. 1) is up

to 50%.

- The fringe contrast is high

and always 100% at exit A1

(translator remark:

independent on the splitting

ratio of the beam splitter).

- The interferogram is free of

false light and all secondary

reflections can be suppressed.

- Both exits (A1 and A2) are

complementary, meaning at

exit A1 the zero order fringe

is bright, at exit A2 it is dark.

In order to make the instrument

usable for people that are not

acquainted with interferometric

work, it shall be described in

maybe greater detail than seems

necessary at first sight.

Working principle:

Let us have a look at fig. 1: the

assembly from lamp Q to baffle

B2 is used to produce a

collimated beam, which is already

given when using a laser as a

source. The beam is divided by

the beam splitter cube into two

coherent parts, beam 1 and 2,

that are capable of interfering.

The beam that is reflected from

the splitting surface inside the

cube, beam 1, creates an image

Q’ of the baffle B1 on the concave

test mirror, which for simplicity is

drawn as spherical.

After reflection from the mirror

surface and transmission through

the small symmetrical biconvex

lens L3, beam 1 forms a spherical

wave with its centre at P1. The

quality of this “reference wave”,

as we might call it, is not

influenced by the defects of the

test mirror, because the reflection

at Q’ is generated by only a small

part of the surface, which can be

regarded as defect free.

Beam 2 passes through lens L3

on the way to the mirror and

illuminates the complete diameter

as a spherical wave. The defects

of the mirror are imprinted on

this wave, forming a second light

wave with origin at P2. The two

wave fronts with centres P1 and

P2 are now mixed by cube W1

and their interference can be

observed at exit A2 or - with a

second beam splitter cube W2 -

at exit A1.

The interferometer does not work

in strict auto collimation, i.e. the

reflected beam 2’ does not

coincide with beam 2. Therefore

the diameter of the usable field of

view of the test mirror/objective

must be bigger than the P1-P2

distance, otherwise it will show

astigmatism and coma, defects

that should not be present on axis

of the test specimen.

Optical parts:

1) The light source Q: we can

use for example a halogen

incandescent lamp with

cylindrical coil, or if not

available even a flashlight /

torch will do. Best of course is

a laser. In order to avoid

extraneous interference all

surfaces should be cleaned

carefully and after adjustment

the parts in direct illumination

by the collimated beam

should be made free of dust

with a soft brush. If the laser

beam is too small for a given

f-ratio, it can be expanded

some without disadvantage

by a single negative lens in

front of the beam splitter.

2) A camera lens of focal length

around 50-mm or a binocular

eyepiece serves as

OBJECTIVE L1.

3) The pinhole B1 is made for

example from a piece of tin

foil with different sized holes

to choose.

4) OBJECTIVE L2 is stepped

down to 5 to 10 mm; its focal

length is chosen such that the

image Q’ of baffle B1 is

smaller than 1/10 of the test

mirror diameter.

5) The beam splitter cube W2 is

only necessary for exit A1 and

should be removed when

using exit A2 (A2 provides

four times the image

brightness of A1). If we don’t

have a cube if necessary we

can cement two Porro prisms

with water or use a thickish

glass plate as beam splitter.

6) The beam splitter cube W1

should have a minimum edge

length of 25 mm. If need be

we can build one by

cementing two suitable Porro

prisms with largely any oil,

for example sun flower oil. If

we used the oil sparingly the

cube is mechanically stable

and compared with

commercial beam splitter

cubes it has the advantage of

an accessible fourth face and

hence the exit A2 becomes

available.

7) The focal length of the

symmetrical biconvex lens L3

is less than 1/20 of the test

mirror’s focal length and

under 15 mm in diameter. Its

defects are compensated

automatically even if it is

tilted in the beam path, hence

a corrected system would not

have any advantage. It

should be mentioned that an

asymmetrical lens (e.g.

plano-convex) can be used.

In this case, however, the

lens has to be adjusted

carefully and the test mirror

f-ratio should be at least 10.

If, because of a small usable

field of view of the test

mirror, the P1-P2 distance

(i.e. beam separation, remark

of the translator) has to be

very small, the lens L3 can be

ground close to the lens

centre.

[Comment KLB: with half

moon beam 2 is cut from

above so that the lower half

of the mirror is NOT

illuminated.]

Assembly:

For lens L3 and test mirror PR we

require adjustment in all three

coordinates. At least one of these

two elements has to be fine

adjustable in height

(perpendicular to the drawing

plane). Further, the centers of all

elements must be adjustable to

the same height.

We begin assembly with the

lamp. Its coil is tilted a small

amount from the interferometer

axis. The diaphragm B1 is placed

at a distance from the lamp that

equals approximately 4.5 times

the focal length of lens L1. We

center the emerging light cone on

the test mirror. Next we insert

the objective L1 and project the

image of the inside wall of the

lamp coil onto baffle B1.

This in turn is projected with L2

onto the centre of the test mirror.

If the objective does not possess

a built in diaphragm we insert

another baffle B2 into the beam

that is adjustable in both

directions perpendicular to the

interferometer axis.

The assembly of both beam

splitter cubes is not critical. Cube

W1 acts on beam 2 just like a

plane parallel plate, which here

can only cause a lateral beam

shift. Beam 1 however, which is

reflected off the splitting surface,

has to be adjusted on the mirror

centre by rotating the cube.

Because we want to keep the

requirements for the field of view

of the test mirror small, we will

choose a small distance between

both beams leaving the cube, for

example 10 mm. The position of

beam 2 is set by moving baffle

B2. The beam separation is

adjusted by moving cube W1

along the direction indicated by

the arrow in Fig. 1.

Finally we insert lens L3 in beam

2 at a distance from W1 equalling

its focal length. Only when testing

fast mirrors we place the beam

splitter cube closer to the lens.

In order to avoid light passing the

lens on its side we may need to

reduce baffle B2 to a smaller

beam diameter. It should also be

small enough so that the light

cone created by L3 does not over-

illuminate the test mirror by

much.

The distance of the test mirror

from L3 equals its radius of

curvature (or its focal length if it

is an astronomical objective with

a plane mirror). Now the

assembly of the interferometer is

finished and we can take on the

alignment.

Fig. 2: Elimination of objectionable reflections

Alignment

As a small tool we need some

strips of stiff paper. We place one

strip under each beam splitter

cube to be able to turn them in

small amounts. Now we move

lens L3 or baffle B2 in the plane

normal to the beam and center

the light cone leaving the lens on

the test specimen. If this an

objective we cover the flat mirror

(Fig. 4) with black paper and

adjust the objective axis with the

help of the lens reflections to lie

on the interferometer axis.

Following this we intersect beam

1 with a white paper strip at P2

and adjust the image formed by

the test mirror/lens of the lens

focus F exactly opposite P1 into

the beam center. This is achieved

by tipping, tilting and moving the

mirror or objective along the

optical axis.

Now we reach the final phase of

adjusting. We look into either exit

A1 or A2 into the interferometer

(take care when using a laser,

translator remark), and we will

see all kinds of reflections: one is

from cube W2 -- it can be moved

by rotating the cube. Another is

from cube W1 (see Fig.2). Finally

there can be reflections from lens

L3; they can be removed by

tilting the lens.

If we were careful during

assembly and adjustment so far,

we can now see the two

diffraction disks from P1 and P2.

P2 is only visible inside the test

objects outline and can be

recognized more easily by moving

our head back 20 to 30 cm.

The following fine adjustment

positions the interferometer or

the test object so that both

diffraction disks have equal size

and coincide. The size is

controlled by changing the L3-PR

distance. The discs are made to

coincide by tipping and tilting the

mirror (or plane mirror if an

objective is being tested) by small

amounts. Another method is to

adjust the lens height of L3 and

rotate cube W1. Doing this the

beam will move on the test

object, but it should not leave it.

This second method is more

convenient but affects the

illumination of the test object.

If we managed to get the two

spots to the same size and to

superimpose we can now see the

interference fringes. To get a

feeling for this phenomenon we

now alter the previous

adjustment steps by very small

amounts. The focus of the beams

that pass the central area of the

test specimen - which is of

biggest interest to us – is called

paraxial focus. We can find it

easily if we bring the center of the

visible ring system to the centre

of the fringe pattern (i.e. get the

bulls eye, translator remark), and

only then adjust the L2-PR

distance. If by accident we lose

the fringe pattern by large

misalignment, it is not advisable

to search for the diffraction disks

at the interferometer exit, but

rather start again from the

beginning of this paragraph.

Fringe pattern

Let us assume the test object is a

perfectly spherical mirror. In this

case with the interferometer at

the centre of curvature the fringe

pattern shows an evenly bright

(exit A1) or dark (A2) surface. If

we now move P1 or P2 sideways

or in height (translator remark:

X,Y coordinates,), straight,

parallel and structure-less fringes

appear (see also the numbered

front cover pictures) regardless of

their orientation. If the test

specimen has surface defects it

clearly shows in the fringes

(Picture 1 and 2).

Pictures 1 and 2

We have to examine these

interferences in greater detail

because we want to know if

maybe the usable field of view is

smaller than P1-P2, and what

defects the test specimen shows

for on axis and tilted rays. The

interferograms are so manifold,

that we can only deal with

spherical aberration, astigmatism

and coma here, and have to

restrict ourselves in most cases to

the optical axis.

Irregular variations of the

wavefront are reflected by

irregular variations in fringe width

and directions. We see an

example in picture 2, the

interferogram of a Fraunhofer

objective of unknown origin. It

shows 1 lambda aberration for

single pass (see pictures 3 and

4).

Pictures 3 and 4

The maximum aberration

following picture 1 is lambda/15.

Of special interest to us is of

course the interferogram of the

spherical aberration for the

central rays, the paraxial focus

(picture 3) and next to it (picture

4 and also picture 2).

Additional parts of the article

mostly dealing with fringe

analysis are omitted here because

electronic data reduction has now

taken the place of visual

geometric analysis. Appropriate

and powerful software is available

today at:

“http://starryridge.com/mediawiki-

1.9.1/index.php?title=Interferogram_Analysis”.

Two final remarks on fringe

photography. To avoid vignetting

a small Kepler telescope with a

power of 2 to 4 between the

interferometer and the camera is

advisable. Further the camera has

to be focused onto the rim of the

mirror under test, otherwise the

fringes get frayed out at their

ends.

Literature

[1] K.-L. Bath, Ein einfaches

Common Path Interferometer,

Optik 36 (172) 349.

[2] Original article in Sterne und

Weltraum, 1973/6, 177 –

180. Translation from German

by Andreas Derwahl with kind

permission of Sterne und

Weltraum, Heidelberg.