High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns

Abstract

Based on the idea of measuring small rotation angles with a parallel interference pattern (PIP), a method is developed to measure large rotation angles accurately. Two parallel PIP's that have different periods are used to measure a rotation angle of an object. The measurement made with a small-period PIP provides a high accuracy, and the measurement made with a large-period PIP provides a wide range. An accurate measurement for wide-range angles is made by combining the two measured values. The accuracy of the phase detection is determined by the periods of two PIP's. Rotation angles from approximately -30 to 30 arc min can be measured with an accuracy of 0.2 arc sec. Analytical results are supported by experimental results.

Simultaneous multi-segmented mirror orientation test system using a digital aperture based on sheared Fourier analysis

“…For the normal application of an angular measurement, laser interferometers [10], and photoelectric autocollimators [11] are standard solutions. Their accuracy is state of the art, but they have limited capability when measuring multiple segments and surface shapes.…”

Novel composite coded pattern for small angle measurement using imaging method

“…• Estimate the value of 'n' described in the relation (9), from the row selected in the color region of Image -A and Image-B using the 'unwrapping procedure' outlined in the following sections.…”

“…In other words, the phase difference '∆α' obtained from the relation (8) is wrapped in the range of -Π to + Π. The true value of the phase difference ∆α uw in an experiment can be larger than ∆α and is given by ∆α uw = ∆α + 2nΠ (9) where n is an integer. In the remaining part of this communication, ∆α uw and ∆α will be referred to as unwrapped and wrapped phase differences respectively.…”

“…The accurate measurement of angle of rotation is thus critically dependent upon the accurate unwrapping of the relative phase difference. The process of unwrapping is a process of determining the value of n shown in the relation (9) and essentially involves addition/ subtraction of proper integer multiples of 2Π to '∆α' obtained from the relation (8).…”

“…They include approaches based on internal reflection effect 4,6 , heterodyne interferometry 5 , double exposure speckle photography 7 , speckle shearing interferometry 8 , parallel interference patters (PIP) 9 , phase characteristics of surface plasma resonance (SPR) 10 e.t.c. .…”