Optical System Design PDF
Preview Optical System Design
Source: Optical System Design 11 CHAPTER Basic Optics and Optical System 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 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 (cid:1) 10°, or alternatively as 350 (cid:1) 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 (cid:1) 5 matrix, and the 5 (cid:1) 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 3 Basic Optics and Optical System Specifications Figure 1.1 Illustration of Num- ber of Resolution Ele- ments Required to Resolve or Distin- guish Alphanumerics 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 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 Figure 1.2 Typical Specifications 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/numberor ƒ/#,where focal length ƒ/number (cid:2) (cid:3)(cid:3)(cid:3) clear aperture diameter 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 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 5 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 (cid:1) 4 (cid:1) 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, (cid:4) (cid:2) 450 nm through (cid:4) (cid:2) 650 nm, as 1 5 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 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 8 Chapter 1 Figure 1.4 Numerical Aperture and ƒ/# 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- 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 9 Basic Optics and Optical System Specifications ty. The ƒ/number at used conjugate is 1/(2(cid:5)NA), 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: Optical system basic Basic system parameters: operational and Object distance performance Image distance specifications and Object to image total track requirements Focal length ƒ/number (or numerical aperture) Entrance pupil diameter Wavelength band Wavelengths and weights for 3 or 5 (cid:4)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 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 Optical system basic operational and Maximum length performance Weight specifications and Environmental: requirements Thermal soak range to perform over (Continued) 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 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 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.
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