ABSTRACT
It is frequently necessary to place a beam splitter in a convergent beam. If a plate is used, it will introduce coma and astigmatism into the axial image. This can be reduced or eliminated by:
Use a pellicle. This is equivalent to a plate of zero thickness. Pellicles are made by forming a nitrocellulose plastic over a flat frame. They are extremely thin, typically about 5 μm. Limited types of coatings may be applied to this rather fragile part. Glass pellicles of perhaps 0.005-in. thick glass are also available. Although thicker than the plastic form, they are more durable and a large variety of coatings may be applied.
Use a cube beam splitter. This is equivalent to a plane plate in the system and they are easily accommodated in the optical design. They are bulky and sometimes there is no way to incorporate them into the mechanical package. In the IR region, a cube is out of the question.
Use a wedge plate. By this technique, axial coma and astigmatism may be substantially reduced.
As seen in Figure 27.1, a plate of thickness T with a wedge angle of θ is in a converging beam. It is a distance P to the image. The plate is at an angle β to a normal to the optical axis. A plate of thickness <italic>T</italic> with a wedge angle of <italic>θ</italic> in a converging beam. It is a distance <italic>P</italic> to the image. The plate is at an angle <italic>β</italic> to a normal to the optical axis. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/fig27_1.tif"/>
For zero astigmatism, De Lang (1957) gives the following value for the wedge angle, θ, in radians: θ = sin β ( cos 2 β ) T 2 ( N 2 − sin 2 β ) P . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq123.tif"/>
Coma is also substantially reduced.
The author once incorporated a beam-splitter into a 10 × microscope objective system. The beam splitter had the following parameters: N = 1.51872 ( N-BK7 glass ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq124.tif"/> B = 45 ∘ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq125.tif"/> T = 0.04 in . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq126.tif"/> P = 14.9473 in . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq127.tif"/>
Using these values in the above equation gives a wedge angle, θ equal to 0.00026186 rad, or 54.0 sec. Using the ZEMAX optimization program, 310and with a perfect lens (a paraxial lens in ZEMAX) of f/4 and effective focal length (EFL) of 20.0, gives a wedge angle of 36.7 sec. Figure 27.2 shows the results of this by means of the spot diagram of the axial image. For comparison, a spot diagram is also presented for a parallel plate. The difference between this computed value and that given by the De Lang formula is the formula is based on third-order theory, whereas the data shown in Figure 27.2 is based upon exact ray tracing. Wedge plate. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/fig27_2.tif"/>
Use two beam-splitters oriented 90° to each other. That is, if an observer looks along the optical axis, they will see two reflected beams at a 90° orientation to each other. A plane plate may be used to displace a beam and is the basis of rotary prism cameras. In this type of camera, a plate is coupled to the film movement such as to cause a displacement equal to the film movement. The problem, in addition to aberrations of the plate, is that this displacement is not a linear function of the plate rotation. Referring to Figure 27.3 that shows the displacement of a plane plate of thickness T and refractive index N, sin I = sin I ′ N , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq128.tif"/> D = T sin ( I − I ′ ) cos I ′ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq129.tif"/> The displacement of a plane plate of thickness <italic>T</italic> and refractive index <italic>N</italic>. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/fig27_3.tif"/> 311 312
For small angles of incidence, D = T I ( N − 1 ) N . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq130.tif"/>
Increasing the refractive index of the prism rotator from N-K5 to N-LAK10 yields a thinner rotary prism, but with nearly the same nonlinear function of displacement vs. rotation. Due to the nonlinear displacement of the plate, a shutter is provided in rotary prism cameras to cutoff the beam to limit 313 314this displacement error. The example given is for a cube prism for a 16-mm film camera. Using the above formula for N-LAK10 glass and D equal to 0.3, one obtains a T value of 0.455.
