PVr-用于光学表面规格的稳健幅度参数 Zygo Christopher J. Evans
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PVr—a robust amplitude parameter for optical
surface specification
Chris J. Evans, MEMBER SPIE
Zygo Corporation
Laurel Brook Road
Middlefield, Connecticut 06455
E-mail: cevans@zygo.com
Abstract. Peak-to-valley departure 共PV兲 is entrenched in optics design
and manufacture as a characterization of an optical figure; modern inter-
ferometers commonly use 1k⫻ 1k detectors, the output of which may not
be well represented by two points. PVr is a newly proposed robust am-
plitude parameter that combines the PV of a 36-term Zernike fit and the
root mean square of the residual. This provides automatic filtering, is
insensitive to system resolution, and relates directly to imaging perfor-
mance via the Marechal criterion. Use of PVr in place of PV is
recommended.
© 2009 Society of Photo-Optical Instrumentation Engineers.
关DOI: 10.1117/1.3119307兴
Subject terms: metrology; interferometry; optical testing.
Paper 080347RR received May 5, 2008; revised manuscript received Feb. 12,
2009; accepted for publication Feb. 18, 2009; published online Apr. 27, 2009.
1 Introduction
Traditionally, optical surfaces have been specified by the
peak-to-valley departure 关共PV兲, height difference between
highest and lowest points on the surface after removal of
piston and tilt for flats and best fit sphere for spherical
surfaces兴 from the nominal surface shape. In some cases,
specifications that relate directly to the particular optical
function in a given application have been developed. Such
cases are in the minority; the majority of optics sold today
are still specified as / N 共e.g., a quarter-wave, tenth-wave,
etc.兲. Such specifications can cause difficulties due, for ex-
ample, to defects and dirt on the test surfaces or in the
interferometer, especially as spatial resolution increases. In
addition, it is not uncommon to find discrepancies between
outgoing quality assurance at an optic’s vendor and incom-
ing inspection by its customer. Interferometers with differ-
ent spatial resolutions and different noise characteristics re-
port different values of PV. Hence, a robust amplitude
parameter 共PVr, where “r” represents “robust”兲 is proposed.
Section 2 discusses the old connection between PV and
optical performance, and Section 3 describes the problems
with modern use of PV as an optical surface specification.
Section 4 introduces the new parameter 共PVr兲 and outlines
its characteristics, before addressing in more detail 共Section
4.5兲 the reasons for its robustness. Standardization is briefly
discussed in Section 5.
Optical surface specifications using such characteristics
as power spectral density functions, structure function,
slopes, or scatter clearly have a direct connection to surface
function. Use of such specifications is encouraged. In those
cases, however, where PV is currently used, replacing it
with PVr may reduce manufacturing costs and the number
of disputes between buyers and sellers over part conform-
ance.
2 PV in the Traditional Optical Shop
Classical opticians finished surfaces on pitch laps and as-
sessed their work using a light box and test plate. Experi-
enced opticians automatically filtered out “noise”—dirt or a
pit in the test plate, for example—and used the shape of the
fringes to assess the PV. The slightly more rigorous ap-
proach using, for example, a Polaroid print of the fringes
and a parallelogram implies similar filtering. Fringe center
finding methods using early laser Fizeau interferometers
did much the same, although with slightly higher spatial
resolution.
How does this filtered PV relate to functional perfor-
mance? In an imaging system, one simple criterion for per-
formance is the diffraction limit. Marechal’s criterion states
that the system will be diffraction limited if the wavefront
is better than / 14 root mean square 共rms兲. Traditional op-
tical manufacturing processes typically “polish out” quite
quickly, and the bulk of the time is spent driving down the
low-order surface aberrations. Considering these low-order
aberrations as an expansion of Zernike terms 共ignoring pis-
ton and tilt兲, we calculate from the definition of the
polynomials
1,2
the ratio of PV to rms term by term 共Table
1兲.
0091-3286/2009/$25.00 © 2009 SPIE
Table 1 PV to rms ratio for low order aberrations.
Aberration PV:rms ratio
Power 3.5
Astigmatism 4.8
Coma 5.6
Third-order spherical 3.4
Trefoil 6.3
Optical Engineering 48共4兲, 043605 共April 2009兲
Optical Engineering April 2009/Vol. 48共4兲043605-1
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