Christiaan H. F. Velzel

Output power and coherence length of stripe-geometry double-heterostructure semiconductor lasers in incoherent feedback

We studied the power characteristic and the coherence length of stripe-geometry double-heterostructure semiconductor lasers with an external cavity. The length of the external cavity was made larger than the coherence length of the laser at threshold, measured without feedback. Some of the experimental results could be explained by a model in which a single laser mode was considered as a van der Pol oscillator. The effect of the external cavity was simulated by adding an external signal to the oscillator. The behavior of the coherence length depends on the mode spectrum and cannot be explained fully by a single-mode model.

Characteristic functions and the aberrations of symmetric optical systems. I: Transverse aberrations when the eikonal is given

We describe the transverse aberrations of a symmetric optical system with a given eikonal (angle characteristic function). The aberrations are expressed in the coordinates of the image field and the pupil parameters according to Schwarzschild. Conditions for freedom from aberrations and for aberrations in the focal plane are considered. We show how the transverse aberrations up to the ninth order can be calculated from eikonal coefficients; we give the conditions under which the eikonal coefficients are identical to the aberration coefficients.

Dependence of third- and fifth-order aberration coefficients on the definition of pupil coordinates

Three pupil-coordinate definitions are considered for the description of aberrations. The corresponding sets of expressions for the third- and fifth-order image-aberration coefficients as well as the third-order pupil-aberration coefficients are presented. We show their interrelations and the connection with eikonal coefficients. One pupil-coordinate definition leads to the occurrence of 9 independent fifth-order image-aberration coefficients; the other two definitions lead to 12 independent fifth-order image-aberration coefficients. We find that the third-order image-aberration coefficients are independent of the choice of pupil-coordinate definition, whereas the third-order pupil-aberration coefficients and the fifth-order image-aberration coefficients do depend on this choice. We show that the case of ideal imaging may imply finite pupil aberrations.

Characteristic functions and the aberrations of symmetric optical systems. II. Addition of aberrations

We describe a method for the calculation of the eikonal coefficients of a symmetric optical system composed of two symmetric subsystems. We consider coefficients of second to tenth order in the direction cosines. The system eikonal is seen to consist of an additive part and correction terms of sixth and higher order. We discuss the interpretation and the magnitude of the correction terms.

Linear ray-propagation models in geometrical optics

Two linear ray-propagation models are discussed. In one model, the ray-direction variables are direction tangents. In the other model, direction cosines are used instead. In particular, the construction of rays to first-order accuracy according to the direction-cosine scheme is explained. The refraction invariance of the pupil coordinate, as defined by Schwarzschild [ SchwarzschildK., Abh. Koenigl. Ges. Wiss. Goettingen Math. Phys. Kl. Neue Folge4, 8– 9 ( 1905)], is highlighted. In the case of imaging, only the rays constructed according to the direction-cosine propagation model satisfy the sine condition. Hence it is this ray-propagation model that retains physical significance beyond the paraxial region. Moreover, it is only the direction-cosine model that is not in contradiction with the impossibility of perfect three-dimensional imaging. Therefore, as a starting point for the theory of aberrations, the direction-cosine model is to be preferred over the direction-tangent model.

Characteristic functions and the aberrations of symmetric optical systems. III: Calculation of eikonal coefficients

We give a complete description of the calculation of the eikonal coefficients of symmetric optical systems. First, we show how to express the eikonal coefficients of each component as functions of the component data and the position of the object and the stop. We decompose each eikonal into meridional and sagittal subseries, and we give a proof of the uniqueness of this decomposition. Second, we give simple formulas to calculate system eikonal coefficients of the sixth order in the direction cosines and a fast algorithm to obtain a good estimate of coefficients of orders higher than the sixth. We conclude with a discussion on pseudoaberrations and their uses and also a generalization of the Seidel formulas for the addition of aberrations.

Sensor-controlled optical assembling

For the assembling of the optical systems with high performance and submicron tolerances it is necessary to optimize the system while it is being assembled. This means that parts of the system must be positioned and fixed with sufficient accuracy, and that the process must be checked by optical measurement. Sensor controlled optical assembly is the combination of these activities, integrated with optical and mechanical design. We expect that sensor controlled optical assembling will make possible the manufacturing of new optical systems with high performance. In this paper we discuss the methods and technologies necessary to implement sensor controlled optical assembling and we give examples of applications. The theoretical background of this work was given in a paper delivered at the SPIE Annual Meeting 1989 in San Diego.

Chromatic aberrations in lens design

In texts on geometrical optics and lens design usually two types of chromatic aberrations are discussed: longitudinal and transverse. From basic considerations on first order geometrical optics follows that, for an axially symmetric system there are three paraxial constants. Therefore three, instead of two types of chromatic aberrations can be discerned. The third, new, chromatic aberration can be called chromatic pupil aberration. We describe the consequences of this aberration for the color correction of optical systems, and show that stable chromatic correction requires the elimination of all three chromatic errors. We give expressions that can be used in the lay-out of optical systems. In teaching geometrical optics it is necessary to determine the generic aberrations of a system of given symmetry from first principles: our treatment of chromatic aberrations is an example of this necessity.

Pattern projection by conventional or diffractive optics: a comparison

Pattern projection is an important application area of diffractive optics, comprising microlithography and laser materials processing. We discuss differences in performance and requirements between pattern projection with conventional imaging optics and with diffractive optics.

Pattern projection by diffractive and conventional optics: a comparison

Diffractive optics can be used for the projection of patterns in, for instance, laser material processing or microlithography. We compare diffractive optics with conventional pattern projection methods with respect to efficiency, resolution and field, influence of coding and illumination. We describe an experiment in diffractive pattern projection with an excimer laser.