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Figure 1: The lens system follows the Cartesian sign convention
Figure 2: Thin lens formula
Applying the above concept, the lens specifications are determined based on the desired magnification and their distances within an afocal zoom system, which is depicted in Figure 1.
Figure 3: Diagram of three-lens afocal zoom system: K1, K3 are converging lenses, and K2 is diverging lens. d(d’) is distance from the second(third) lens to the first(second) principal plane H(H’).
© 1997 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(97)02204-6]
As a result, the focal lengths of each lens is fixed, so as the distances between lenses d1 and d2 change, M varies. The variation of M with respect to lens separation distance is described in Figure 2.
Figure 4: Diagram of three-lens afocal zoom system: top diagram shows that M will be increased when d1 decreases and d2 increases; whereas, the bottom diagram shows that M will be decreased when d1 increases and d2 decreases. © 1997 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(97)02204-6]
By fixing the distances d1 and d2 we can design a fixed optical lens system at any desired magnification. For instance, the lens system has F1 = 45 mm, F2 = -300 mm, F3 = 68 mm, and d1 = 22 mm, d2 = 25 mm yields a magnification of 4.3x and a working distance of about 76 mm — which represents the distance from subject’s eye to the front lens26. Following this idea, we are able to design for a specific magnification needed to capture a particular image area; in this case, we chose to use a lens system with a 3.34x magnification and 100 mm working distance.
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