Thin-Lens Theory

Vector scanning of laser beams is critical to the success of stereolithography, laser marking, CAD-output-to-microfilm and many other industrial applications. The design of a vector scan lens system can assume many different configurations. This paper will discuss pre-objective, and post-objective alternatives for two and three axis scanning. Various parameters required for system specification are reviewed and the basic configuration of the two axis scan head is presented. The pre-objective scan f-theta lens, its scan distortion, telecentric options, and single origin scan systems are described. Fixed focus and dynamic focus post-objective systems are presented discussing the relative merits of each approach and noting the limitations of each design solution. Data presented describe limiting field sizes for fixed focus systems, and limiting f-numbers for thin lens systems. Thin lens design equations for three post-objective configurations are presented with suggested optimization techniques for overall system layout. Examples of pre-objective and post-objective scan lens systems as well as pre- configured systems are presented.

The characteristics of an optical system vary depending on wavelength and ambient temperature. Based on the thin-lens approximation, we investigate the conditions for stabilizing an optical system against wavelength and temperature variations at the same time. The conditions are applied to designing a laser scanning system consisting of two lenses. The change in the effective focal length of the scanning system against wavelength and temperature variations is very small, as expected.Keywords: Optical system design, Stabilized optical system, Laser scanning system, Achromatization, AthermalizationOCIS codes: (080.2740) Geometric optical design; (080.3630) Lenses; (220.3620) Lens system design

So far, we have considered refracting imaging systems: a spherical refracting surface in Chapter 1, a thin lens in Chapter 2, and a plane-parallel plate in Chapter 3. Now we consider the imaging properties of a spherical reflecting surface, i.e., a spherical mirror. These properties can be obtained in a manner similar to that for a spherical refracting surface. However, the geometry of the problem is different since now a ray incident on the surface is reflected back into the same medium containing the incident ray, instead of being refracted into another medium. Accordingly, it is instructive to draw object and image rays and not blindly use the imaging and aberration relations appropriate for a reflecting surface. In this chapter, we give the relations describing the primary aberrations of a spherical mirror for an arbitrary position of the aperture stop. These relations are applied to specific cases, one when the aperture stop is located at the mirror and the other when it is located at its center of curvature. It is shown that, in the first case, field curvature and distortion are zero. In the second case, coma, astigmatism, and distortion are zero. A numerical problem illustrates these results. <strong>4.2 PRIMARY ABERRATION FUNCTION</strong> Consider an imaging system consisting of a spherical mirror of radius of curvature <i>R</i> and focal length <i>f</i>&#x2032;. Let the aperture stop and the corresponding exit pupil of the system be located as indicated in Figure 4-1. The line joining the center of curvature <i>C</i> of the mirror and the center of the aperture stop (and, therefore, the center <i>O</i> of the exit pupil) defines the optical axis of the system. Consider an object lying at a distance <i>S</i> from the vertex <i>V</i>₀ of the mirror. Let the height of an object point <i>P</i> from the optical axis be <i>h</i>. The distance <i>S</i>&#x2032; and the height <i>h</i>&#x2032; of its Gaussian image <i>P</i>&#x2032; are given by (4-1) and (4-2a) (4-2b) respectively, where <i>M</i> is the magnification of the image.

We analyze the dispersion effect of the focal length of low-index thin lenses by using scalar diffraction and finite difference time domain (FDTD) methods. We compare the dispersion results obtained by using these methods with reported experimental results, and the well-known analytical formula for focal length (f) of diffractive lenses as a function of wavelength ( λ ) , f ( λ ) = f 0 λ 0 λ where f0 is the designed focal length for wavelength λ0. We show that when the analytical formula is applied to thin flat lenses with low-refractive index, the results are accurate for small numerical aperture (NA) up to 0.2. For larger NA, the error between the analytical approximation and the FDTD analysis remains around 8% over a wide range of NA.

A closed-form analytical expression is derived for a partially coherent dark hollow beam (DHB) propagating through an arbitrary real ABCD optical system in a turbulent atmosphere. The average intensity of the beam in the output plane is investigated in the presence of, respectively, a thin lens image system and a two-lens system along the optical path. For a special thin lens image system, the partially coherent DHB and the fully coherent DHB have the same evolution properties, and the comparative analysis is made between the propagation of the focused DHB and the collimated DHB for direct propagation in turbulence to show the effect of the thin lens on the average intensity. As for the two-lens system, the effects of the lens systems, the structure constant in the turbulent medium and the parameters of the incident beam on the average intensity are evaluated and illustrated. The result shows that different lens systems and propagation parameters can evidently affect the evolution properties of the beam.

In this paper, we investigate the focusing properties and focal shift of a partially coherent vortex cosine-hyperbolic-Gaussian beam (PCvChGB) passing through a lens system. Based on the extended Collins formula, the analytical expression for a PCvChGB propagating through a thin lens is derived in detail. By using the obtained formula, the influences of the spatial coherence length, the Fresnel number, and the initial beam parameters on the focusing properties and the focal shift of a PCvChGB are discussed numerically. It is shown that the average intensity distribution in the focal region and the focal shift of the focused PCvChGB are strongly affected by the above factors. The obtained results could be beneficial for applications of vortex cosine-hyperbolic-Gaussian beam (vChGB) beams in beam shaping and atom optics.

The interface between optical design and fine-mechanical design is a creatively fertile stage in the design of an optical system. The optical designer learns `What the system is all about' and the fine-mechanical engineer is liberated creatively by finding out what the priorities are. On the other hand, optical tolerancing as a discipline, which is an attractive mix of optical physics at one end and hard-nosed mechanical pragmatism at the other, has a relatively fragmented literature. It is the purpose of this paper to (1) Point out some cultural contrasts between optical engineers, mechanical engineers and physicists in this context, (2) To present a new method of displaying the optical surface sensitivities so that one may identify datum surfaces in an intuitive way and (3) To summarize some useful formulae which provide a key to the mounting of optical components. Together these three aspects illustrate the scenery of this fertile terrain.

The author states that<i>Optics</i>serves the student ophthalmologist "as preparation for his study of refraction of the eye and as background for his understanding of physiological optics and visual physiology." The broad field of elementary geometrical optics is treated thoroughly, with particular emphasis on the ophthalmic aspects of this subject. An attempt has been made to restrict the use of mathematics, and the mathematics present does not require unusual aptitude. Orientation is provided by a brief introductory review of the physical nature of light. A clear explanation of the vergence concept results in an intuitive understanding of image-formation by thin lenses. Thin-lens theory is applied to the problems of ocular refraction, and the characteristics of the optical system of the eye are described. Equations and diagrams assist in presenting the theory of image-formation by optical systems and by spherical refracting surfaces. The aberrations of spherical surfaces and the astigmatism

In previous papers the author has shown that lens systems focusing wide-angle, large diameter illumination beams do not focus the output beam-waist at the location predicted by the standard paraxial lens imaging equations. The paraxial equations fail because they are meant to apply to rays that lie in the plane of the lens system axis of symmetry- meridional rays, whereas illumination beams are composed of skew or out-of-plane rays. The skew-ray equations derived in the author's earlier papers turn out to provide the correct description of the non-imaging optics of focused illumination beams. The skew-ray beam equations allow the basic lens system parameters; focal length and conjugate distances to be determined from the input beam diameter and divergence angle. The lens system parameters calculated from the skew-ray beam equations are optimal in the sense that they define an optical system that theoretically satisfies the fundamental requirement of conservation of E'tendue. Therefore if the appropriate aberrations of this theoretically optimum illumination beam optical system can be corrected the system should approach 100 percent geometric throughput. This paper discusses how certain types of imaging optical systems can be used as models for the design of equivalent non-imaging illumination beam- transformer optical systems. The use of these image system models permits a direct assessment of the importance of the classical image aberrations in the design of highly efficient illumination beam optics. The paper also outlines design methods for optimizing illumination beam optics using existing imaging optics software. The conclusion is that practical illumination optics beam-transformers can be designed with throughputs above 99 percent, even using a single lens.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A novel polymer-based fluid-actuated variable focal length microlens system with a wide field-of-view (FOV) and large numerical aperture is designed and fabricated using standard photolithographic and silicon micromachining techniques. A flexible polydimethylsiloxane (PDMS) membrane is used to form the lens surface and is actuated by fluidic pressure applied by an external syringe pump. This lens system is capable of working in dual mode, forming either a double convex (DCX) or a double concave (DCV) lens. The relationship between the focal length (f) and FOV of the fabricated dynamic lens system as a function of the volume of the fluid pumped into or out of the lens chamber is investigated. The focal length of the dynamic lens system demonstrated in this paper could be tuned in the range of 75.9 to 3.1 mm and −75.9 to −3.3 mm for the DCX and DCV lens configurations, respectively. The FOV for this lens system was found to be in the range of 0.12 to 61° for DCX lens and 7 to 69° for DCV lens. The smallest F-number (f/#) that could be achieved using this dynamic lens is 0.61, which corresponds to the numerical aperture value of 0.64.

An electrostatic four cylinder electrode electron optical lens system is described. It is designed for experiments where beam energy scanning is needed. The lens system was investigated experimentally and results are given. The characteristics of the lens system have also been calculated theoretically following a procedure known from the light optical lens design. These calculations have justified the design procedure and showed that the composite lens system characteristics can be directly computed very successfully.

The paper presents an efficient approach to design a Cassegrain optical system for spaceborne remote sensing. The optical system has a focal length of 1000mm, F number of 5.6, the range of spectral band 0.4~0.9μm, and field of view 3°, distortion smaller than 1%. The effect of central obscuration on the image quality in the optical reflective system design is analyzed. It provides proof for reasonable choose of obscuration ratio in optical system design. With the help of CODE V software, the final two designs are obtained by a simple and quick optimization step, the image quality of which reaches the diffraction limit. It is shown the second structure style is designed by making the surface of primary mirror in the Cassegrain system hyperbolic, adding two high order aspheric surfaces and removing two lenses from lens compensator, and therefore the second with the simpler structure, smaller size and lighter weight, comparing with the first structure style, can be used in spaceborne remote sensing.

As reported in Nature journal, the super resolution gigapixel camera of Duke University was highlighted on June, 2012 from Wall Street Journal and mass media. According to the reports, Duke gigapixel camera system was developed with big grant for the purpose of military operation and surveillance under the supports of DARPA because of the needs of US military. And this gigapixel camera is expected to promote new big market in the area of national defense and vision technology in the near future. In this paper, optical structural study was first proceeded to make a sense of whole optical ray mechanism so that the lens system could be optimized effectively by utilizing the data from structural study. And we also studied optomechanical design for building whole camera system.

We have developed a computer program which allows analysis of soft contact lens flexure without assuming a priori that the posterior surface of the lens aligns with the central anterior cornea. Such analysis leads to the conclusion that thin low-minus lenses entrap tear layers of low volume (about 5.5 microliter) and minimum power, whereas low-plus lens systems can develop tear layers of greater volume (about 9.5 microliter), and significant power (about -2.00 D). The later finding supports clinical impressions that plus lenses "lose" power when placed on the eye. In some cases our data suggest that the lens posterior surface closely aligns with the anterior cornea, whereas in other cases such alignment is unlikely. It also appears that mathematical models for the simultaneous flexure of front and back radii of soft lenses may be described for specific lens designs. This current study suggests that delta r2 congruent to 2 delta r1 describes the relation for low-plus lenses, and delta r2 congruent to 0.75 delta r1 is the relation for low-minus lenses.

Hilda Gertrude Kingslake/Rudolf Kingslake