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Article
Gear manufacturing using power-skiving method on six-axis CNC turn-mill machining center
Power-skiving is an efficient method for the manufacturing of high accuracy gears, particularly internal gears. However, dedicated power-skiving machine tools are normally very expensive. Accordingly, the pres...
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Book
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Chapter
Optically Stable Systems
Utilizing an image orientation function, this chapter proves the finding of Schweitzer et al. (Appl Opt 37:5190–5192, 1998) that only two types of optically stable reflector system exist, namely preserving or ...
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Chapter
Hessian Matrix of Optical Path Length
Chapter 14 presented a method for determining the Jacobian matrix of the optical path length (OPL) of a skew ray.
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Chapter
Raytracing Equations for Paraxial Optics
Conventional paraxial optics, sometimes known as Gaussian optics, uses \( 2 \times 2 \) ...
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Chapter
Ray Aberrations
In Chap. 5, imaging was considered to be ideal. In other words, the rays originating from an object point and passing through an optical system converge to t...
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Chapter
Jacobian Matrix of Boundary Variable Vector X̄i with Respect to System Variable Vector X̄sys
The system variable vector \( {\bar{\text{X}}}_{{\text{sys}}} \) ...
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Chapter
Prism Design Based on Image Orientation
One of the main functions of prisms is that of image reorientation. In designing a prism to produce an image with a particular orientation, most researchers use the trial-and-error method proposed by Smith (p....
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Chapter
Optical Path Length and Its Jacobian Matrix
The optical path length (OPL) is an essential property of optical systems since it determines the phase of the light and governs the interference and diffraction of the rays as they propagate.
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Chapter
Hessian Matrices of Ray R̄i with Respect to Incoming Ray R̄i-1 and Boundary Variable Vector X̄i
As discussed in the previous chapter, the study of optical systems basically involves either systems analysis or systems design. Systems design is the reverse problem of systems analysis.
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Chapter
Mathematical Background
The homogeneous coordinate notation is a powerful mathematical tool used in a wide range of fields, including the motion of rigid bodies [1, 2], robotics [3], gearing theory [4], and computer graphics [5]. Previo...
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Chapter
Geometrical Optical Model
In geometrical optics, the problem of modeling an optical system in an efficient and systematic manner is highly challenging.
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Chapter
Cardinal Points and Image Equations
2 × 2 raytracing matrices are extremely useful in geometrical optics. In this chapter, the 2 × 2 raytracing matrix approach is used to describe the path of a paraxial meridional ray traveling along the ...
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Chapter
Jacobian Matrices of Ray R̄i with Respect to Incoming Ray R̄i–1 and Boundary Variable Vector X̄i
In automated optical design systems, the Jacobian matrix of an optical quantity with respect to the system variables is generally estimated using the Finite Difference (FD) method.
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Chapter
Prism Analysis
Prisms are common optical elements containing only flat boundary surfaces. In spectral instruments, their function is to disperse light, while in other applications, they are used to displace, deviate or re-or...
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Chapter
Determination of Prism Reflectors to Produce Required Image Orientation
Optical prisms provide the ability to output an image with a certain orientation and to relocate the exit ray in a given manner. In designing a prism, one of the most important tasks is that of determining the...
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Chapter
Point Spread Function, Caustic Surfaces and Modulation Transfer Function
Chapter 3 described the use of a ray-counting method to derive the point spread function (PSF), modulation transfer function (MTF) and spot diagram of an opt...
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Chapter
Wavefront Aberration and Wavefront Shape
The study of optical systems may be considered from two different perspectives, namely systems analysis and systems design, respectively.
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Chapter
Hessian Matrix of Boundary Variable Vector X̄i with Respect to System Variable Vector X̄sys
As discussed in Chap. 8, the system variable vector \( {\bar{\text{X}}}_{{\text{sys}}} \) ...
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Chapter
Skew-Ray Tracing of Geometrical Optics
In geometrical optics (or ray optics), light propagation is described in terms of “rays”, where each ray is regarded as an idealized narrow bundle of light with zero width (Cornbleet, Proc IEEE 71:471–502 (198...
