Optical: systems and elements – Diffraction – From zone plate
Reexamination Certificate
1999-08-27
2001-07-17
Henry, Jon (Department: 2872)
Optical: systems and elements
Diffraction
From zone plate
C359S572000, C359S569000
Reexamination Certificate
active
06262844
ABSTRACT:
I. FIELD OF THE INVENTION
This invention relates to optical systems employing stepped diffractive surfaces (SDSs). More particularly, in accordance with certain of its aspects, the invention relates to the athermalization of optical systems by means of one or more stepped diffractive surfaces.
II. BACKGROUND OF THE INVENTION
A. Athermalization
As known in the art, the optical properties of an optical system normally vary with changes in temperature as a result of: (i) changes in the indices of refraction of the optical materials used in the system, (ii) changes in the shape of the optical elements used in the system, (iii) changes in the dimensions of the housing used to hold the optical elements, and (iv) changes in the wavelength or frequency of the light source employed in the system.
Such changes in optical properties with changes in temperature are undesirable and extensive efforts have been made to solve this problem, examples of which can be found in the following patents and literature references: Londono et al., U.S. Pat. No. 5,260,828; Borchard, U.S. Pat. No. 5,504,628; Behrmann et al., “Influence of temperature on diffractive lens performance,”
Appl. Opt.,
1993, 32: 2483-2489; D. S. Grey, “Athermalization of Optical Systems,”
JOSA,
1948, 38:542-546; T. H. Jamieson, “Thermal effects in optical systems,”
Opt. Eng.,
1981, 20:156-160; Kryszcynski et al., “Material problem in athermalization of optical systems,”
Opt. Ens.,
1997, 36:1596-1601; Londono et al., “Athermalization of a single-component lens with diffractive optics,”
Appl. Opt.,
1993, 32:2295-2302; Tamagawa et al., “Dual-band optical systems with a projective athermal chart: design,”
Appl. Opt.,
1997, 36:297-301; and Handbook of Optics, 2nd ed., M. Bass editor, McGraw-Hill, Inc., New York, 1995, volume I, 32.15-32.16.
The thermal behavior of an optical surface can be described in terms of the surface's “optothermal” coefficient defined as:
X
Φ
=
1
Φ
ⅆ
Φ
ⅆ
T
(
I
)
where “&PHgr;” is optical power and “T” is temperature.
For a refractive surface separating a first medium having an index of refraction n
1
and a second medium having an index of refraction n
2
, X
&PHgr;,R
is given by:
X
Φ
,
R
=
1
(
n
2
-
n
1
)
(
ⅆ
n
2
ⅆ
T
-
ⅆ
n
1
ⅆ
T
)
-
α
(
II
)
where &agr; is the coefficient of thermal expansion of the substrate medium (i.e., the solid medium which forms the refractive surface) and where the paraxial optical power of the surface, &PHgr;
R
, is given by:
Φ
R
=
(
n
2
-
n
1
)
R
0
where R
0
is the vertex radius of the refractive surface.
The corresponding expression for a diffractive kinoform surface is:
X
&PHgr;,K
=−2&agr; (III)
where again &agr; is the coefficient of thermal expansion of the substrate medium (in this case, the solid medium which forms the kinoform surface) and where the paraxial optical power of the surface, &PHgr;
K
, is given by:
Φ
K
=
8
N
λ0
(
D
0
)
2
where D
0
is the clear aperture diameter of the kinoform surface, N is the total number of zones within the clear aperture, and &lgr;
0
is the system's nominal operating wavelength.
Table 1 sets forth values of X
&PHgr;,R
and X
&PHgr;,K
for various optical materials which can be used in the visible, infra-red (IR), or ultra-violet (UV) regions of the spectrum, as well as ratios of X
&PHgr;,K
to X
&PHgr;,R
for these materials. For Si and Ge, the fact that the optothermal coefficients for kinoforms are much smaller than those for refractive components can make it difficult to athermalize a refractive system composed of these materials with a kinoform. For these as well as the other materials in this table, the use of a kinoform can complicate the athermalization process since unlike stepped diffractive surfaces (see below), kinoforms introduce optical power into the system at the system's nominal operating wavelength (&lgr;
0
).
B. Stepped Diffractive Surfaces
FIGS. 1A and 1B
illustrate optical elements employing stepped diffractive surfaces
13
a
and
13
b
of the type with which the present invention is concerned. To simplify these drawings, opposing surfaces
15
a
and
15
b
of these elements have been shown as planar. In the general case, the opposing surfaces can have optical power or can be another stepped diffractive surface, if desired.
As shown in these figures, stepped diffractive surfaces
13
comprise a plurality of concentric planar zones
17
(also referred to as “steps”) which are orthogonal to optical axis
19
. The zones lie on a base curve which is shown as part of a circle in
FIGS. 1A and 1B
, but in the general case can be any curve of the type used in optical design, including conics, polynomial aspheres, etc. The base curve may also constitute a base surface in cases where the concentric planer zones are not axially symmetric, i.e., where their widths are a function of &thgr; in an (r, &thgr;, z) cylindrical coordinate system having its z-axis located along the system's optical axis. For ease of reference, the phrase “base curve” will be used herein and in the claims to include both the axially symmetric and axially non-symmetric cases, it being understood that in the non-symmetric case, the base curve is, in fact, a base surface. In either case, the base curve can be characterized by a vertex radius Ro which, as discussed below, can be used in calculating the paraxial properties of the stepped diffractive surface.
The stepped diffractive surfaces of the invention are distinguished from digitized (binary) kinoforms by the fact that the sag of the stepped diffractive surface changes monotonically as the zone number increases. The sag of the surface of a binary kinoform, on the other hand, always exhibits a reversal in direction at some, and usually at many, locations on the surface. This is so even if the base curve for the binary kinoform has a monotonic sag.
Quantitatively, the zones of the stepped diffractive surface preferably have widths (w
i
) and depths (d
i
) which satisfy some or all of the following relationships:
|d
i
|\|d
i+1
|<2.0, for
i
=1 to
N−
2;
|d
i
|≡j
i
&lgr;
0
/|(
n
2
−n
1
)|, for
i
=1 to
N−
1;
and
w
i
/&lgr;
0
>1.0, for
i
=1 to
N;
where “j
i
” is the order of the ith zone of the stepped diffractive surface (j
i
>1), N is the total number of zones (N=6 in FIGS.
1
A and
1
B), and “n
1
” and “n
2
” are the indices of refraction of the media on either side of the stepped diffractive surface, with light traveling through the stepped diffractive surface from the n
1
medium to the n
2
medium.
The “j
i
” nomenclature is used in the above equations to indicate that the working order of the stepped diffractive surface can be different for different zones. In many cases, the same working order will be used for all zones; however, for manufacturing reasons, it may be desirable to use different working orders for some zones, e.g., if the zone width wi would become too small for accurate replication with a constant working order, especially, for a constant working order of 1. In this regard, it should be noted that j
i
can be made greater than 1 for all zones, again to facilitate manufacture of the stepped diffractive surface by, for example, reducing the overall number of zones comprising the surface and, at the same time, increasing the depth and width of the individual steps.
Like the monotonic sag characteristic, the |d
i
|\|d
i+1
|<2.0 characteristic distinguishes the diffractive surfaces of the invention from digitized (binary) kinoforms, where |d
i
|\|d
i+1
| is normally greater than 2.0 for at least some steps, i.e., where the kinoform profile returns to the base curve. The |d
i
|≡j
i
&lgr;
0
/|(n
2
−n
1
)| characteristic in combination with the requirement that j
i
≧1 also distinguish the stepped diffractive surfaces
Henry Jon
Klee Maurice M.
KSM Associates, Inc.
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