The real aberration properties (all orders) and correction abilities of optical aspherical surfaces of arbitrary shape are
insufficiently investigated due to the lack of exact aberration theory. Here we derive and investigate an exact analytical distortion function for axis-symmetric aspherical surfaces of arbitrary shape that describes correctly image distortion for the whole object space without any approximations. We prove that in
the object and image spaces of every aspherical refracting or reflecting surface at fixed stop position there is in general
one orthoscopic object surface and one conjugate image surface. In addition we offer formulae for determination of
object and image orthoscopic surface coordinates in every refracting or reflecting axis-symmetric optical surface with
known coordinates and continuous first derivative on the whole profile. To verify the distortion correction we use the commercial program OSLO. The differences between our results and these
obtained by OSLO are less than 1.10-8 mm.
Using these exact formulae we investigate the real shape and location of the orthoscopic object and image surfaces as a
function of stop position in different reflecting and refracting aspherics. The results can be used by optical designers in the process of synthesis of orthoscopic optical systems.
The process of optical design today is both an art and a science mainly due to the lack of exact and suitable aberration
theory. In this paper we propose an exact (without any approximations) analytical aberration theory. It describes exactly
the relations between the on-axis image aberrations and on-axis object aberrations via so called relative parameters, real
aperture incidence angles, real aperture slope angles, refraction indexes and object distance. The image field aberrations
(distortion, astigmatism, tangential curvature, sagittal curvature and field curvature) are described in a mathematically
exact way by means of relative parameters, real incidence angles and slope angles of the chief rays, refraction indexes,
object distance and corresponding object aberrations. For the image tangential coma and image sagittal coma we propose
differential formulae. To verify the correction of every single aberration we use the commercial program OSLO. The
differences between our and OSLO results for each aberration (except for the tangential and sagittal coma) are less than
1x10-8 mm. In addition we propose some exact aberration's correction algorithms for a very distant object and variety of
constructive design solutions which confirm the truth of the proposed theory.
We derive and investigate an exact analytical paraxial longitudinal chromatic function for axis-symmetric optical
systems. We prove the existence of two conjugate pairs of achromatic points in the object and image space of every
centered optical system (in general they are two, but in some cases they can be missing or their number can be one or
infinite-dimensional) and derive formulae for determination of their position in object and image spaces. On the base of
this function we develop an exact analytical design method for paraxial chromatic correction in axis-symmetric optical
systems. In addition we show some examples.
We derive an exact analytical image astigmatic function for aspherical and hyper-aspherical surfaces of arbitrary shape
that describes correctly (without any approximations) image astigmatism for the whole object space and investigate this
function for two general cases: in the presence and in the absence of object astigmatism. So we discover the boundary
astigmatism correction ability of aspherical surfaces. We prove that in general there are two anastigmatic points on each
chief ray in every aspherical surface. We find as well analytical expressions for anastigmatic and extreme points of the
function and its vertical and horizontal asymptotes. As a result we prove that in the object and image space of every
refracting aspherical surface at each stop position there are two pairs of anastigmatic surfaces one of them coincides with
the refracting surface itself. In the object and image space of every reflecting aspherical surface at each stop position
there is in general one anastigmatic surface which coincides with the reflecting surface itself. There are special cases
when the whole space of the reflecting aspherical surface is anastigmatic.
KEYWORDS: Objectives, Digital video discs, Data storage, Collimators, Aspheric lenses, Optical storage, Optical components, Refraction, Data processing, Optical discs
One way to amplify the optical memory capacity is to increase simultaneously the numerical aperture of the reading and
writing objective, to decrease the laser wavelength and to use optical discs with multilayer construction. In this paper we
show how to optimize and design single lens aspheric objectives with high and super high numerical aperture for red
and blue DVD. We demonstrate the image quality of constructions of an objective for red DVD with high numerical
aperture 0.9, an objective for blue DVD with super high numerical aperture 0.95 and collimators for red and blue DVD.
KEYWORDS: Image quality, Aspheric lenses, Diffraction, Differential equations, Optical design, Data storage, Objectives, Digital video discs, Data processing, Optical storage
Optical systems for data storage and processing of information have diffraction limited image quality. This requires an exact fulfillment of aplanatic conditions on the whole system aperture and usually leads to the introduction of two more adjacent aspherical surfaces. For exact defmition of these aspheric surface shapes it is necessary to solve numerically a system of two first-order differential equations. For this purpose, one can use Runge-Kutta or Adams-Bashforth-Moulton algorithms or combination of them both. However, solutions often can not be found, particularly for systems with high and super high numerical aperture. If the solution is not found, it is not clear whether it exists or not and what is the reason for the lack of solution. We propose an analytical solution of Wassermann-Wolf differential equations for aplanatism that overcomes such disadvantages. We show that the solution of the system of two Wassermann-Wolf first-order differential equations is mathematically equivalent to the consecutive solution of a set of independent linear
equations and the most important factor of the lack of solution is the critical angle of incidence of aperture rays at the two aspherical surfaces. The proposed algorithm allows reliable and effective design of aplanatic optical systems containing two neighboring aspherical surfaces with high and super high numerical aperture and diffraction limited image quality for an object at infinity. We illustrate the successful application of the algorithm to the design of blue DVD objective with super high (0.95) numerical aperture and diffraction limited image quality.
In Multi-Spot Diffusing (MSD) configuration, the communication channel can be considered virtually ideal at data rates of hundreds of Mbps. Thus, the main concern is power efficiency. We propose transceiver optical designs that allow for a reconfigurable transmitter output and independent communication channels. Transmitter employs multiple light sources that can be turned on and off independently. This way, optical signal is provided only where it is needed, which optimizes power usage. Receiver utilizes an imaging optical system and segmented photodetector, thus performing direction diversity reception. We show that when maximum ratio combining is employed for the electric signals processing and power efficient modulation schemes like L-PPM are used significant power savings can be obtained.
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