1. 1
Preliminary results on the parabolic primary mirror making study for the
application in Newtonian Reflecting Telescope
H.D.S Amaradasa1
, S.S.Abeywickrama2
, E.M.ranatunga3
, G.D.K.Mahanama4
Department of Physics, University of Ruhuna, Matara, Sri Lanka
4
Corresponding Author- mahanama@phy.ruh.ac.lk
Abstract
A study of mirror making was initiated with the aim of designing a Newtonian reflecting
telescope. Parabolic mirror of 15 cm aperture and 1.49 m focal length was made using a glass
blank. Flat Soda-Lime glass was selected for this task and two identical disks were cut and
inspected for any imperfection on surfaces. Inferior glass was used as the tool and other was
used as the mirror.One side of a flat glass disk (one selected for the mirror) was grinded into
the parabolic concave shape usingseries of Silicon Carbide (SiC) and Aluminum Oxide
(Al2O3) abrasives of different grit sizes. Ferric Oxide (Fe2O3) and optical pitch were used in
polishing process. Depth of the mirror was checked using a parallel beam of light. Uniformity
of the parabolic shape was tested using Focult and Ronchi tests. Deviations from the required
parabola were investigated by employing Texerau’s method as a data reduction method. It
was found that parabolic shape of the glass is satisfying astronomical optical standards of
Rayleigh and Donjan&Couder criteria confirming the quality of mirror prepared by this
method.
Key words:Glass disk, Silicon carbide,reflector,abrasive,Parabolic shape

2. 2
Preliminary results on the parabolic primary mirror making study for the
application in Newtonian Reflecting Telescope
Abstract
1. Introduction
Ever since Galileo took a Dutch invention and adapted it to astronomical use, astronomical
telescope making has been an evolving discipline.Although the types of telescopes that
amateurs build vary widely, the most popular telescope design is the Newtonian reflector
described by Russell W.Porteri
.The Newtonian has the advantage of being a simple design
that allows for maximum size for the minimum expense. The most important step of
telescope making is the mirror figuring. Parabolic mirror figuring techniques used in
telescope making require being reliable and effective in grinding a uniform depression in a
flat surface. Various methods are followedby both professional and amateur astronomers to
grind different sizes of mirrors. Major objective of this research is to adopt an economical
technique to produce mirrors utilizing maximum amount of local resources maintaining the
figure with precision and standards required for optical astronomy. Here we report the
preliminary results obtained in the study of mirror making techniqueof grinding two identical
glass disksusinga series of abrasives.
2. Procedure
Glass blanks were cut from Soda Lime Flat glass. Relatively inexpensiveness, chemically
stableness and thermal coefficient of 9.5 were main characteristics considered in selecting
Soda Lime Flat glass.Two glass blanks of dimensions 0.15 m diameter and 0.012 m thickness
were cut and edges were beveled. Blanks were inspected for air bubbles and blemishes close
to the surfaces.The blank with fewerblemishes was used as the mirror and other was used as
the tool.
Rough grinding was initiated fixing the tool on a horizontal rotatable surface.Paste of
water and Silicon Carbide (SiC) of particle size 125 microns was poured on the tool
surface.With mirror on top, themirror was moved outward about 40% of its diameter over the
tool, concentrating most of the grinding actions on the center of the mirror and the edge of the
tool.Straight strokes were taken such that the center of the mirror travels along an

3. 3
imaginarychord.After twenty Chordalstrokesii
,mirror and the toolwererotatedin 45 degrees to
opposite directions and process was repeated replacing the abrasive paste. After 2 hours of
grinding focal length of the mirror was calculated by measuring thelength of center of
curvature.To measure the center of curvature, a point light source was placed on focal axis of
the mirror and position of the mirror was adjusted to get the reflected image next to the
source.When thereflected image was identical in size to the source, distance between
thesource and themirror was measured.Depth of the mirror was checked after each hour of
grinding until it reached required focal length of 1.49 m. Penciltestiii
was used to determine
thecontact between the mirror and the tool during grinding.In this test a radial grid pattern
was drawn onto the surface of the mirror using a pencil. Then normal strokes were given and
pencil marks were disappeared. By watching the rate and points of smudging and
disappearance across the mirror, deduced where the mirror and tool were in close contact and
where they were not.Grinding procedure was repeated decreasingthe particle size of the
abrasives from 68,44,25 microns,respectively.Fine grinding was initiated with 12
micronAluminum Oxide (Al2O3) taking center over center strokes and continued from 5 and
3 microns. Ferric Oxide (Fe2O3) and optical pitch were used in polishing process. Lap of
optical pitch was molded utilizing the tool as the base and square grooves were cut in the lap.
Placing lap over mirror W-Strokesii
were taken so spherical surface was grinded and polished
into a smooth parabolic surface. Uniformity of the parabolic shape was tested using
Focult iv
and Ronchiiv
test. Deviations from the required parabola were investigated by
employing Texerau’sv
method.

4. 4
2.1 Testing process
According to Raleighvi
criteria for a standard mirror maximum wavefront error must not
exceed a quarter wave and Danjon-Coudervi
condition, the radius of the circle of least
aberration should be comparable with that of the theoretical diffraction disk.Mirror was tested
for both conditions from Focult test and Ronchitest.Both tests were performed placing a point
light source at the radius of curvature.TheFocult test was performed placing a knife edge at
the radius of curvature andthemirror was masked from a Coudermaskvi
of four zones.Light
source was positioned stationary at the center of curvature and knife edge was adjusted
longitudinally, along focal axis of the mirror. Positions of the knife edge related to occulted
zones were measured.Two sets of readings were taken for different rotations of the
mirror.Radius of the circle of least aberration and maximum wave front error were studied by
plotting data reduced from Texerau’s method. For the Ronchi test the knife edge was
replaced by a 100 lines per inch Ronchi grating .Reflected light from mirror was observed
through the grating. An interference pattern was observed and symmetry of the generated
pattern was inspected.
3. Results
Table 1: Zonal Radii and Knife edge readings (inches)
Zonal Radii and Knife edge positions for two rotations of the mirror given in Table 1 was
inserted to Texerau’s method and obtained Airy disk radii-Average radii of zones
andWavelengths–edge zone radii characteristics.Graphical representation of mirror surface
across zones is shown in Figure 1(a).The wavelengths–edge zone radii characteristics
indicated that the surface of the mirror has a peak value of 1/5.44wavelengths.As shown in
shown in Figure1 (b) all the points inAiry disk radii-Average radii of zones characteristicsare
distributed between -1 and 1.
Zone
#
Zone
%
ZoneCentre Zone
Edge
Knife
Edge D1
Knife
Edge D2
1 35.4 1.061 1.500 0.793 0.792
2 61.2 1.837 2.121 0.870 0.869
3 79.1 2.372 2.598 0.901 0.900
4 93.5 2.806 3.000 0.908 0.900

5. 5
-1.0000
0.0000
1.0000
0.000 1.000 2.000 3.000
Airydiskradii
Average radii of zones
-0.2500
0.0000
0.2500
0.000 1.000 2.000 3.000 4.000
Wavelengths(560nm)
Edge zone radii
Figure 2: Interference pattern generated in the Ronchi Test
As shown in Figure (2) interference pattern produced in the mirror surface was observed in
the Ronchitest.Interference pattern was produced using a monochromatic light source placed
at the center of curvature.Grating was fixed to illuminate the source and adjusted around
inside and outside of the radius of curvature until distinct pattern is observed.The
Photographin the Figure (2) was taken 0.083 m outside the center of curvature.
4. Conclusion
All Airy disk radii of the mirror are between -1 and 1 proving themirror can converge light in
focal point minimizingtransverse or longitudinal aberrations and wave-front error has shown
that the highest peak in the mirror surface is less than thequarter waveconfirming themirror is
meeting the conditions of Raleigh criteria and Danjon-Coudercondition.In addition the
Ronchi test has shown that the curvature of the mirror is evenly distributed along the
radius.Based on these results it can be concluded that the technique utilized in this research is
effective and reliable in producing precise optics for Astronomical telescopes.
Figure 1-(b) Graph of Airy disk radii and Edge radii of zonesFigure 1-(a) Graph of Airy disk radii andAverage radii

6. 6
References
i
Vandewttering, Mark T.Telescope basics. 2001.
ii
Berry, Richard. Build Your Own Telescope. Wiscosin : Scribdner, 1985
iii
Upton, John D. www.atm-workshop.com. The Dykem test. [Online] [Cited: 04 13, 2015.]
http://www.atm-workshop.com/dykem-test.html.
iv
Malacara, Daniel.Optical Shop Testing. s.l. : A John Wiley & Sons, Inc., 2007. ISBN: 978-0-471-
48404-2 .
v
Shroeder, D.J.Astronomcal Optics. London : Acadamic Press.Inc, 1987. ISBN 0-12-629805.
vi
Taylor, H.Denis. The Adjustment and Testing of Telescope Objectives. Newcastle : Pearson & Co,
1946.