1.21Visit Us OnLine! www.mellesgriot.comFundamental OpticsMaterial PropertiesOptical SpecificationsGaussian Beam OpticsOptical CoatingsTHE OPTICAL ENGINEERING PROCESSDetermine basic system parameters, such as magnification and object/image distancesUsing paraxial formulas and known parameters, solve for remaining valuesPick lens components based on paraxially derived valuesEstimate performance characteristics of systemDetermine if chosen component values conflict with any basic system constraintsDetermine if performance characteristics meet original design goalsENGINEERING SUPPORTMelles Griot maintains a staff of knowledgeable, experienced applications engineers at each of our facilities worldwide. The information given in this chapter is sufficient to enable the user to select the most appropriate catalog lenses for the most commonly encountered applications. However, when additional optical engineering support is required, our applications engineers are available to provide assistance. Do not hesitate to contact us for help in product selection or to obtain more detailed specifications on Melles Griot products.Even though several thousand different optical components are listed in this catalog, performing a few simple calculations will usually determine the appropriate optics for an application or, at the very least, narrow the list of choices.The process of solving virtually any optical engineering problem can be broken down into two main steps. First, paraxial calcula- tions (first order) are made to determine critical parameters such as magnification, focal length(s), clear aperture (diameter), and object and image position. These paraxial calculations are covered in the next section of this chapter.Second, actual components are chosen based on these paraxial values, and their actual performance is evaluated with special attention paid to the effects of aberrations. A truly rigorous performance analysis for all but the simplest optical systems generally requires computer ray tracing, but simple generaliza- tions can be used, especially when the lens selection process is confined to a limited range of component shapes.In practice, the second step may reveal conflicts with design constraints, such as component size, cost, or product availability. System parameters may therefore require modification.Because some of the terms used in this chapter may not be familiar to all readers, a glossary of terms is provided beginning on page 1.29.Finally, it should be noted that the discussion in this chapter relates only to systems with uniform illumination; optical systems for Gaussian beams are covered in Chapter 2, Gaussian Beam Optics.IntroductionChpt. 1 Final a 7/30/99 2:39 PM Page 1.2Visit Us Online! www.mellesgriot.com11.3Fundamental OpticsGaussian Beam OpticsOptical SpecificationsMaterial PropertiesOptical CoatingsParaxial FormulasSIGN CONVENTIONSThe validity of the paraxial lens formulas is dependent on adherence to the following sign conventions: For lenses:(refer to figure 1.1)sis 1 for object to left of H (the first principal point)sis 5 for object to right of Hs is 1 for image to right of H (the second principal point)s is 5 for image to left of Hm is 1 for an inverted imagem is 5 for an upright image For mirrors: fis 1 for convex (diverging) mirrorsfis 5 for concave (converging) mirrorssis 1 for object to left of Hsis 5 for object to right of Hs is 5 for image to right of Hs is 1 for image to left of Hm is 1 for an inverted imagem is 5 for an upright image When using the thin-lens approximation, simply refer to the left and right of the lens.sfFffront focal pointrear focal pointprincipal pointsfobjectHvimageH Fshhf=lens diameterm =s/s = h/h = magnification or conjugate ratio, said to be infinite if either s or s is infinitev=arcsin (f/2s)h=object heighth =image heights=object distance, positive for object (whether real or virtual) to the left of principal point Hs =image distance (s and s are collectively called conjugate distances, with object and image in conjugate planes), positive for image (whether real or virtual) to the right of the principal point Hf=effective focal length (EFL) which may be positive (as shown) or negative. f represents both FH and HF, assuming lens to be surrounded by medium of index 1.0Note location of object and image relative to front and rear focal points.Figure 1.1Sign conventionsChpt. 1 Final a 7/30/99 2:39 PM Page 1.31.41Visit Us OnLine! www.mellesgriot.comFundamental OpticsMaterial PropertiesOptical SpecificationsGaussian Beam OpticsOptical CoatingsobjectF1F2image20066.7Figure 1.2Example 1 (f = 50 mm, s = 200 mm, s = 66.7 mm)objectF1F2imageFigure 1.3Example 2 (f = 50 mm, s = 30 mm, s = 475 mm)1 f= 1 s1 s.+m = s s= h h.f = m(s + s )(m + 1)f = sm m + 1f = s + sm + 2 + 1 ms (m + 1) = s + s21s= 1f1s1s= 1501200s = 66.7 mmm = ss= 66.7200= 0.33(or real image is 0.33 mm high and inverted).44(1.1)(1