Unified Optical Scanning Technology

Chapter 4.3.5.5 - Scanner Devices and Techniques: Image Rotation and Derotation

4.3.5.5    Image Rotation and Derotation    The rotation of an isotropic point spread function (PSF) about its optical axis is nominally undetectable. However, if the illuminating beam forms a PSF that is nonisotropic geometrically or polarized, or if an array or group of points is to be scanned, some arrangements can cause rotation of the images about the projected axis (the principal ray of the scanned beam or group.) For a nonrotation condition, consider the postobjective monogon scanner of Figure 4.7, which is illuminated coaxially with a grossly overfilled beam. The rectangular boundary of the mirror delimits the reflected beam to exhibit a substantially uniform near-field intensity distribution. During mirror rotation, this rectangular near-field cross section maintains the same relationship to the Φ- or Θ- direction. And the projected scanned focused beam also maintains a fixed (x-y) orientation on the image surface. Thus, with the mirror boundary delimiting the illuminating beam, the focal point (having a diffraction-limited sinc2x,y form of PSF) maintains the same relation-ship to the (x-y) coordinates on the image surface of Figure 4.7. That is, it does not rotate.

If, however, the same scanner is underfilled with, for example, an elliptical cross section gaussian beam, this smaller input beam (not the mirror boundary) establishes the elliptical contour of the reflected beam. Here, the focused elliptical Gaussian spot rotates about its projected axis directly with mirror rotation [Gin,Lev].To see this, consider the major axis of the illuminating ellipse to be vertical, along the z-axis of the center-scan position. When the rotating mirror of Figure 4.7 is in this position (as illustrated), the major axis of the near-field reflected beam falls along the y-axis. (The focused Gaussian ellipse, Fourier transformed in quadrature, arrives with its major axis along the x-axis.) When the scanner is rotated through 90°, the major axis of the incident illuminating beam remains along the z-axis, while the beam encounters the rotated mirror such that the major axis of the reflected beam near-field now appears along the x-axis. (This transforms to a focused elliptical spot whose major axis forms along the y-axis.) The reflected beam is rotated about its principal z-axis by the same angle as the rotation of the scanner. Similarly, if the scanner is illuminated with polarized or multiple beams to form an array of scanned spots, the imaged polarization or array angle will rotate about its z-axis directly with the mirror. This effect is identical in the pyramidal polygon of Figure 3.6. Each mirror forms a marginal segment of the centered mirror of Figure 4.7, imparting the same rotation about its axis to the reflection of the illuminating beam.

This effect does not occur, however, for the mirror mounted per Figure 4.8 or for the prismatic polygon of Figure 3.6. It is also independent of preobjective or postobjective operation. When the principal rays of the input and scanned beams are in a plane that is normal to the axis of rotation, execution of scan does not alter the image (except for possible aperture vignetting or alteration of the reflection characteristics during scan). In the above cases of radial symmetry (Section 3.4.1), the incident angles remain constant while the focused images rotate. Here (in extreme radial asymmetry), the incident angles change while the image develops no rotation. Although mirrored scanners seldom operate between these extremes, holographic scanners can, creating possible complication with, for example, polarization

Fig. 4.8 Postobjective mirror with reflective surface on rotating axis (typical galvanometer mount).Scan angle Θ is twice rotational angle Φ (m = 2). From [Bei3].

states. This is manifest in the variation in diffraction efficiency of gratings for the p and s polarizations (holographic or otherwise) when they are rotated [Bei1].

To implement derotation, complementary rotation is interposed in the path to cancel rotation caused by the scanner. The characteristic of a coaxial image rotator is that it inverts an image [Lev]. This results in two rotations of the image per rotation of the component. Thus, when counterrotated at ½ the speed of the scanner, a rotator such as the Dove prism can provide coaxial image derotation. Whereas the use of the Dove prism is limited preferably to operation in collimated light,* alternatives are not only available for such use but are adaptable to serve in converging or diverging light [Lev,Bro]. They include a three-mirror assembly that simulates by reflection the refractive paths of the Dove prism, a cylindrical/spherical optical relay, and a Pechan prism, a compact arrangement of prisms having reflective surfaces for operation in noncollimated light. To optimize the location of the rotator, consider the discussion in Section 3.3.1 regarding the propagation of angular errors in view of the resolution invariant. To minimize the transfer of paraxial angular errors that might be introduced by fabrication or

mechanical rotation tolerances, the rotator must be located preferably in advance of any beam expansion optics required for system operation. Not only does this allow use of smaller aperture rotational optics, but the pointing errors due to imperfect rotation of the system are reduced by a factor equal to the beam-expansion magnification.

* Converging or diverging light that refracts at plane surfaces oblique to the optical axis develops spherical aberration, astigmatism, and coma (notably in the Dove prism, having surfaces at substantive obliquity to the optical axis) [Lev, Bro].

 

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