49 research outputs found
Autocollimating compensator for controlling aspheric optical surfaces
A compensator (null-corrector) for testing aspheric optical surfaces is
proposed, which enables i) independent verification of optical elements and
assembling of the compensator itself, and ii) ascertaining the compensator
position in a control layout for a specified aspheric surface. The compensator
consists of three spherical lenses made of the same glass. In this paper, the
scope of the compensator expanded to a surface speed ~f/2.3; a conceptual
example for a nominal primary of Hubble Space Telescope is given. The
autocollimating design allows significant reducing difficulties associated with
practical use of lens compensators.Comment: Accepted Monthly Notices of RA
A purely reflective large wide-field telescope
Two versions of a fast, purely reflective Paul-Baker type telescope are
discussed, each with an 8.4-m aperture, 3 deg diameter flat field and f/1.25
focal ratio.
The first version is based on a common, even asphere type of surface with
zero conic constant. The primary and tertiary mirrors are 6th order aspheres,
while the secondary mirror is an 8th order asphere (referred to here for
brevity, as the 6/8/6 configuration). The D_80 diameter of a star image varies
from 0''.18 on the optical axis up to 0''.27 at the edge of the field (9.3-13.5
mcm).
The second version of the telescope is based on a polysag surface type which
uses a polynomial expansion in the sag z, r^2 = 2R_0z - (1+b)z^2 + a_3 z^3 +
a_4 z^4 + ... + a_N z^N, instead of the common form of an aspheric surface.
This approach results in somewhat better images, with D_80 ranging from 0''.16
to 0''.23, using a lower-order 3/4/3 combination of powers for the mirror
surfaces. An additional example with 3.5-m aperture, 3.5 deg diameter flat
field, and f/1.25 focal ratio featuring near-diffraction-limited image quality
is also presented.Comment: 14 pages, 6 figures; new examples adde
On the evolution of a stellar system in the context of the virial equation
The virial equation is used to clarify the nature of the dynamic evolution of
a stellar system. Compared to the kinetic equation, it gives a deeper but
incomplete description of the process of relaxation to a quasi-stationary
state, which here means the fulfillment of the virial theorem. Analysis shows
that the time to reach the virial equlibrium state is about two to three
dozen dynamic time periods . Namely, during the virial ratio, the
mean harmonic radius, and the root-mean-square radius of the system fluctuate,
and then the first two characteristics stabilize near their equilibrium values,
while the root-mean-square radius continues to grow (possibly ad infinitum).
This indicates a fundamentally different behavior of the moment of inertia of
the system relative to the center of gravity and its potential energy, leading
to the formation of a relatively small equilibrium core and an extended halo
Two-mirror Schwarzschild aplanats. Basic relations
It is shown that the theory of aplanatic two-mirror telescopes developed by
Karl Schwarzschild in 1905 leads to the unified description both the prefocal
and the postfocal systems. The class of surfaces in the ZEMAX optical program
has been properly extended to ascertain the image quality in exact
Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate
Ritchey-Chretien and Gregory-Maksutov aplanatic telescopes reveals a noticeable
advantage of the former at fast focal ratio of the system.Comment: 19 page
Quasi-Optimal Filtering in Inverse Problems
A way of constructing a nonlinear filter close to the optimal Kolmogorov -
Wiener filter is proposed within the framework of the statistical approach to
inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions,
produces stable and efficient solutions by relying solely on the internal
resources of the inverse theory. The exact representation is given of the
Feasible Region for inverse solutions that follows from the statistical
consideration.Comment: 9 pages, 240 K