Accurate measurement of the dihedral angle of a corner cube

Measuring corner cube reflectors through ray tracing of a reflected wavefront

The corner cube plays a key role in many advanced optical systems as the critical retrieval component, while the errors such as dihedral deviation will lead to unacceptable results. We present a method to obtain the right-angle plane deviation of the corner cube only by measuring and calculating the normal incident reflection wavefront. The calculation process is an iterative method of ray tracing based on the corner cube reflection process. The three-dimensional shape of the right-angle plane of the corner cube can be obtained accurately by this method. The proposed method is easy to implement and reliable, and it avoids the complicated operation of the traditional measurement method, which can also be applied to the measurement of the errors in the assembly and adjustment process where corner cube reflectors are used.

External right-angle measurement using a two-autocollimator system

We report on a non-contact method for external right-angle measurement using two autocollimators. A precise mathematical model is deduced to evaluate and deduct the measuring error. The values measured with our method are very coincident compared with the results measured by a ZYGO interferometer. The measuring accuracy is superior to 0.1 arcsec for the right-angle errors within 3.0 arcsec and becomes 0.4 arcsec for the extended right-angle errors within 8.0 arcsec. This method can be widely used in situations for external right-angle measurement, such as angle measurement for the body of torsion balance and test mass in spaceborne laser interferometry.

Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset

A method based on phase-shifting Fizeau interferometry is presented with which retroreflectors with large incoming-outgoing beam separations can be tested. The method relies on a flat Reference Bar that is used to align two auxiliary mirrors parallel to each other to extend the aperture of the interferometer. The method is applied to measure the beam coalignment of a prototype Triple Mirror Assembly of the GRACE Follow-On Laser Ranging Interferometer, a future satellite-to-satellite tracking device for Earth gravimetry. The Triple Mirror Assembly features a lateral beam offset of incoming and outgoing beam of 600 mm, whereas the acceptance angle for the incoming beam is only about ±2 mrad. With the developed method, the beam coalignment of the prototype Triple Mirror Assembly was measured to be 9 μrad with a repeatability of below 1 μrad.

Designs of multipass optical configurations based on the use of a cube corner retroreflector in the interferometer

We describe designs of the multipass optical configurations of an interferometer with high spectral resolution with respect to 6, 12, and 24 times more optical passes than the conventional Michelson interferometer. In each design, a movable cube corner retroreflector is combined with a folding reflector group (FRG) as the interferometer's moving combination to implement the multipass optical configuration with the characteristic of surface division. Analyses reveal that when there are 12 or more optical passes, the net effect of the ray's angular deviation of the entire moving combination amounts to only the alignment error of one of the reflectors in the FRG, demonstrating the self-aligning property of the interferometer.

External measurement of dihedral right angles with cyclic optical configuration

A new technique for external measurement of dihedral right angles is presented. An expanded, collimated, and linearly polarized He-Ne laser beam (632.8 nm) from a Fizeau interferometer is launched into a cyclic path optical configuration (CPOC) in which the counterpropagating p and s polarization components traverse the same optical path in opposite directions. A right-angled component (RAC), with its plane surfaces forming the right angle, is set to externally reflect the counterpropagating p and s components of the CPOC in nearly the same directions but with a lateral separation. In a plane normal to the right-angle edge of the RAC, the laterally separated collimated beams have angular separation, which is equal to twice the error in the dihedral right angle. Another CPOC setup is used to recombine the beams by reducing the lateral shear to zero. Error in right angle is calculated from the spacing of the resulting two-beam Fizeau fringes. Methods for overcoming the restriction of measurement accuracy due to beam aperture limitation and the effects of the positional tilt of the RAC have been discussed. Results of validation experiments are presented.

Effect of retroreflection on a Fizeau phase-shifting interferometer

Phase errors in a Fizeau phase-shifting interferometer caused by multiple-reflected beams from a retroreflective optics, such as a corner cube and a right-angle prism, are studied. Single- and double-pass configurations are presented, and their measurement results are compared. An attenuator is not needed in a double-pass configuration because light is reflected by the retroreflective optics twice and the reference surface once and hence the intensities match. It is more accurate to test a corner cube or a right-angle prism in a double-pass configuration than in a single-pass configuration. Simulations and experimental results are presented.