optical system design

Basic Optics and Optical System Specifications 1 CHAPTER 1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Source: Optical System Design 2 Chapter 1 This chapter will discuss what a lens or mirror system does and how we specify an optical system. You will find that properly and completely specifying a lens system early in the design cycle is an imperative ingre- dient required to design a good system. The Purpose of an Imaging Optical System The purpose of virtually all image-forming optical systems is to resolve a specified minimum-sized object over a desired field of view. The field of view is expressed as the spatial or angular extent in object space, and the minimum-sized object is the smallest resolution element which is required to identify or otherwise understand the image. The word “spa- tial” as used here simply refers to the linear extent of the field of view in the plane of the object. The field of view can be expressed as an angle or alternatively as a lateral size at a specified distance. For example, the field of view might be expressed as 10 ϫ 10°, or alternatively as 350 ϫ 350 m at a distance of 2 km, both of which mean the same thing. A good example of a resolution element is the dot pattern in a dot matrix printer. The capital letter E has three horizontal bars, and hence five vertical resolution elements are required to resolve the letter. Hori- zontally, we would require three resolution elements. Thus, the mini- mum number of resolution elements required to resolve capital letters is in the vicinity of five vertical by three horizontal. Figure 1.1 is an exam- ple of this. Note that the capital letter B and the number 8 cannot be distinguished in a 3 ϫ 5 matrix, and the 5 ϫ 7 matrix of dots will do just fine. This applies to telescopes, microscopes, infrared systems, camera lenses, and any other form of image-forming optics. The generally accepted guideline is that approximately three resolution elements or 1.5 line pairs over the object’s spatial extent are required to acquire an object. Approximately eight resolution elements or four line pairs are required to recognize the object and 14 resolution elements or seven line pairs are required to identify the object. There is an important rule of thumb, which says that this smallest desired resolution element should be matched in size to the minimum detector element or pixel in a pixelated charged-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS)–type sensor. While Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications Basic Optics and Optical System Specifications not rigorous, this is an excellent guideline to follow for an optimum match between the optics and the sensor. This will become especially clear when we learn about the Nyquist Frequency in Chap. 21, where we show a digital camera design example. In addition, the aperture of the system and transmittance of the optics must be sufficient for the desired sensitivity of the sensor or detector. The detector can be the human eye, a CCD chip, or film in your 35-mm camera. If we do not have enough photons to record the imagery, then what good is the imagery? The preceding parameters relate to the optical system performance. In addition, the design form or configuration of the optical system must be capable of meeting this required level of performance. For example, most of us will agree that we simply cannot use a single magnifying glass element to perform optical microlithography where submicron line-width imagery is required, or even lenses designed for 35-mm pho- tography for that matter. The form or configuration of the system includes the number of lens or mirror elements along with their relative position and shape within the system. We discuss design configurations in Chap. 8 in detail. Furthermore, we often encounter special requirements, such as cold stop efficiency, in infrared systems, scanning systems, and others. These will be addressed later in this book. Finally, the system design must be producible, meet defined packag- ing and environmental requirements, weight and cost guidelines, and sat- isfy other system specifications. How to Specify Your Optical System: Basic Parameters Consider the lens shown in Fig. 1.2 where light from infinity enters the lens over its clear aperture diameter. If we follow the solid ray, we see that 3 Figure 1.1 Illustration of Num- ber of Resolution Ele- ments Required to Resolve or Distin- guish Alphanumerics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications 4 Chapter 1 it is redirected by each of the lens element groups and components until it comes to focus at the image. If we now extend this ray backwards from the image towards the front of the system as if it were not bent or refracted by the lens groups, it intersects the entering ray at a distance from the image called the focal length. The final imaging cone reaching the image at its center is defined by its ƒ/number or ƒ/#, where ƒ/number ϭ You may come across two other similar terms, effective focal length and equivalent focal length, both of which are often abbreviated EFL. The effec- tive focal length is simply the focal length of a lens or a group of lenses. Equivalent focal length is very much the same; it is the overall focal length of a group of lens elements, some or all of which may be separat- ed from one another. The lens is used over a full field of view, which is expressed as an angle, or alternatively as a linear distance on the object plane. It is important to express the total or full field of view rather than a subset fo c a l le ng t h ᎏᎏᎏ clear aperture diameter Figure 1.2 Typical Specifications Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications Basic Optics and Optical System Specifications of the field of view. This is an extremely critical point to remember. For example, assume we have a CCD camera lens covering a sensor with a 3 ϫ 4 ϫ 5 aspect ratio. We could specify the horizontal field of view, which is often done in video technology and cinematography. However, if we do this, we would be ignoring the full diagonal of the field of view. If you do specify a field of view less than the full or total field, you absolutely must indicate this. For example, it is quite appropriate to specify the field of view as ±10°. This means, of course, that the total or full diagonal field of view is 20°. Above all, do not sim- ply say “field of view 10°” as the designer will be forced to guess what you really mean! System specifications should include a defined spectral range or wave- length band over which the system will be used. A visible system, for example, generally covers the spectral range from approximately 450 nm to 650 nm. It is important to specify from three to five specific wave- lengths and their corresponding relative weights or importance factors for each wavelength. If your sensor has little sensitivity, say, in the blue, then the image quality or performance of the optics can be more degraded in the blue without perceptible performance degradation. In effect, the spectral weights represent an importance factor across the wavelength band where the sensor is responsive. If we have a net spec- tral sensitivity curve, as in Fig. 1.3, we first select five representative wave- lengths distributed over the band, ␭ 1 ϭ 450 nm through ␭ 5 ϭ 650 nm, as shown. The circular data points represent the relative sensitivity at the specific wavelengths, and the relative weights are now the normalized area or integral within each band from band 1 through band 5, respec- tively. Note that the weights are not the ordinate of the curve at each wavelength as you might first expect but rather the integral within each band. Table 1.1 shows the data for this example. Even if your spectral band is narrow, you must work with its band- width and derive the relative weightings. You may find some cases where you think the spectral characteristics suggest a monochromatic situa- tion but in reality, there is a finite bandwidth. Pressure-broadened spec- tral lines emitted by high-pressure arc lamps exhibit this characteristic. Designing such a system monochromatically could produce a disastrous result. In most cases, laser-based systems only need to be designed at the specific laser wavelength. System packaging constraints are important to set at the outset of a design effort, if at all possible. These include length, diameter, weight, dis- tance or clearance from the last surface to the image, location and space 5 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications 6 Chapter 1 for fold mirrors, filters, and/or other components critical to the system operation. Sets of specifications often neglected until it is too late are the envi- ronmental parameters such as thermal soak conditions (temperature range) that the system will encounter. Also, we may have radial thermal gradients, which are changes in temperature from the optical axis outward; diame- Figure 1.3 Example of Spectral Sensitivity Curve Wavelength, nm Relative sensitivity Relative weight 450 0.05 0.08 500 0.2 0.33 550 1.0 1.0 600 0.53 0.55 650 0.09 0.16 TABLE 1.1 Example of Spectral Sensitiv ity and Relative Wavelength Weights 8 Chapter 1 object nor the image is at infinity? The traditional definition of focal length and ƒ/# would be misleading since the system really is not being used with collimated light input. Numerical aperture is the answer. The numerical aperture is simply the sine of the image cone half angle, regardless of where the object is located. We can also talk about the numeri- cal aperture at the object, which is the sine of the half cone angle from the optical axis to the limiting marginal ray emanating from the center of the object. Microscope objectives are routinely specified in terms of numerical aperture. Some microscope objectives reimage the object at a finite distance, and some have collimated light exiting the objective. These latter objectives are called infinity corrected objectives, and they require a “tube lens” to focus the image into the focal plane of the eye- piece or alternatively onto the CCD or other sensor. As noted earlier, the definition of focal length implies light from infinity. And similarly, ƒ/number is focal length divided by the clear aperture diameter. Thus, ƒ/number is also based on light from infinity. Two terms commonly encountered in finite conjugate systems are “ƒ/number at used conjugate” and “working ƒ/number.” These terms define the equivalent ƒ/number, even though the object is not at infini- Figure 1.4 Numerical Aperture and ƒ/# Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications Basic Optics and Optical System Specifications ty. The ƒ/number at used conjugate is 1/(2иNA), and this is valid whether the object is at infinity or at a finite distance. It is important at the outset of a design project to compile a specifica- tion for the desired system and its performance. The following is a can- didate list of specifications: 9 Basic system parameters: Object distance Image distance Object to image total track Focal length ƒ/number (or numerical aperture) Entrance pupil diameter Wavelength band Wavelengths and weights for 3 or 5 ␭s Full field of view Magnification (if finite conjugate) Zoom ratio (if zoom system) Image surface size and shape Detector type Optical performance: Transmission Relative illumination (vignetting) Encircled energy MTF as a function of line pairs/mm Distortion Field curvature Lens system: Number of elements Glass versus plastic Aspheric surfaces Diffractive surfaces Coatings Sensor: Sensor type Full diagonal Number of pixels (horizontal) Number of pixels (vertical) Pixel pitch (horizontal) Pixel pitch (vertical) Nyquist frequency at sensor, line pairs/mm Packaging: Object to image total track Entrance and exit pupil location and size Back focal distance Maximum diameter Optical system basic operational and performance specifications and requirements Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications 10 Chapter 1 Basic Definition of Terms There is a term called first-order optics. In first-order optics the bending or refraction of a lens or lens group happens at a specific plane rather than at each lens surface. In first-order optics, there are no aberrations of any kind and the imagery is perfect, by definition. Let us first look at the simple case of a perfect thin positive lens often called a paraxial lens. The limiting aperture that blocks the rays beyond the lens clear aperture is called the aperture stop. The rays com- ing from an infinitely distant object that passes through the lens clear aperture focus in the image plane. A paraxial positive lens is shown in Fig. 1.5. The rays coming from an infinitely distant point on the optical axis approach the lens as the bundle parallel to the optical axis. The ray that goes along the optical axis passes through the lens without bending. However, as we move away from the axis, rays are bent more and more as we approach the edge of the clear aperture. The ray that goes through the edge of the aperture parallel to the optical axis is called the marginal ray. All of the rays parallel to the optical axis focus at a point on the Maximum length Weight Environmental: Thermal soak range to perform over Thermal soak range to survive over Vibration Shock Other (condensation, humidity, sealing, etc.) Illumination: Source type Power, in watts Radiometry issues, source: Relative illumination Illumination method Veiling glare and ghost images Radiometry issues, imaging: Transmission Relative illumination Stray light attenuation Schedule and cost: Number of systems required Initial delivery date Target cost goal Optical system basic operational and performance specifications and requirements (Continued) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Basic Optics and Optical System Specifications [...]... very important constant in the optical system is the optical invariant or Lagrange invariant or Helmholtz invariant It has a constant value throughout the entire system, on all surfaces and in the spaces between them The optical invariant defines the system throughput The basic characteristic of an optical system is known when the two main rays are traced through the system: the marginal ray going... optical invariant is significantly larger than the system optical invariant, and a lot of light is stopped by the system The implications of the optical invariant and etendue on radiometry and photometry will be discussed in more depth in Chap 14 The magnification of a visual optical system is generally defined as the ratio of the angles subtended by the object with or looking through the optical system. .. Optics and Optical System Specifications Basic Optics and Optical System Specifications 11 optical axis in the focal plane The rays that are coming from a nonaxial object point form an angle with the optical axis One of these rays is called a chief ray, and it goes through the center of the lens (center of the aperture stop) without bending A common first-order representation of an optical system is... and Optical System Specifications Basic Optics and Optical System Specifications 19 Figure 1.14 Optical Power and Focal Length of a Single Lens Element going from the edge of the object through the center of the aperture stop These rays are shown in Fig 1.15 The optical invariant defines the relationship between the angles and heights of these two rays through the system, and in any location in the optical. .. the optical system magnifies or increases the object M times, the viewing angle will be decreased M times In systems analysis, the specification of the optical invariant has a significant importance In the radiometry and photometry of an optical system, the total light flux collected from a uniformly radiating object is proportional to I 2 of the system, commonly known as etendue, where I is the optical. .. where I is the optical invariant For example, if the optical system is some kind of a projection system that uses a light source, then the projection system with its optical invariant defines the light throughput It is useful to compare the optical invariant of the light source with the invariant of the system to see how much light can be coupled into the system It is not necessarily true that the choice... representation of an optical system is shown in Fig 1.6 What we have here is the representation of any optical system, yes, any optical system! It can be a telescope, a microscope, a submarine periscope, or any other imaging optical system Figure 1.5 Paraxial Positive Lens Figure 1.6 Cardinal Points of an Optical System Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)... chief ray that exits the optical system is extended backwards until it crosses the optical axis Both definitions are synonymous, and it will be valuable to become familiar with each Let us assume that we have an optical system with a lot of optical components or elements, each of them having a known clear aperture diameter There are also a few mechanical diaphragms in the system The question is, which... reserved Any use is subject to the Terms of Use as given at the website Basic Optics and Optical System Specifications Basic Optics and Optical System Specifications 25 Figure 1.22 Lateral Displacement of a Ray Introduced by a Tilted Plane Parallel Plate t d ϭ (n Ϫ 1) ᎏ n When a plane parallel plate is tilted in the optical system, as in Fig 1.22, then the ray incident at an angle, ␪, is displaced laterally... subtended by the object with or looking through the optical system to the angle subtended by the object without the optical system or looking at the object directly with unaided vision In visual optical systems where the human eye is the detector a nominal viewing , distance without the optical system when the magnification is defined as unity is 250 mm The reason that unity magnification is defined at a . lens system early in the design cycle is an imperative ingre- dient required to design a good system. The Purpose of an Imaging Optical System The purpose of virtually all image-forming optical systems. as given at the website. Source: Optical System Design 2 Chapter 1 This chapter will discuss what a lens or mirror system does and how we specify an optical system. You will find that properly. and Optical System Specifications Basic Optics and Optical System Specifications optical axis in the focal plane. The rays that are coming from a nonaxial object point form an angle with the optical