Now a Kepler telescope can be set up , which consists of two lenses with 40mm focal length . The first lens is mounted 40mm in front of the WFS , and the second lens is initially mounted 80mm in front of the first lens . In this roughly pre-aligned state , the wavefront shows a tilt of 0.5mrad and a curvature radius of 0.85m . Aligning the second lens of the Kepler telescope in the lateral and axial directions , again tilt is minimised and spherical power of the wavefront is transmitted through the telescope . In this way , the Kepler telescope can be quickly set up and precisely aligned to an afocal configuration . If tilt and defocus resulting from residual misalignments are subtracted , it is found that the setup consisting of collimating lens and Kepler telescope has a “ corrected ” wavefront rms of 0.027 µ m ( on 5mm pupil diameter ). This corresponds to a Strehl ratio of 0.92 , i . e . the setup is well diffraction limited .
Sensitivity of the alignment signal In the above scenario , where the light emitted by the fibre is collimated by the collimating lens , the sensitivity of the wavefront tilt and refractive power need to be considered . To assess stability , the wavefront data is continuously recorded for 5 minutes , and the standard deviation of the temporal signals are calculated ( shown in the graph below ): σTilt = 0.2 µ rad ; σD = 0.06mdpt . Using the above noted relations between lateral displacement and tilt , and between axial displacement and curvature radius , these numbers translate into a theoretical sensitivity of the focus position measurement of ca . 12nm in the lateral direction and ca . 220nm in the axial direction ( for a focal length of ƒ = 60mm of the collimation lens ).
Phase plate and spatial filtering In the second stage of the experiment , a phase plate ( optical window with certain surface aberrations ) is placed as a test object in the object plane of the telescope . The WFS now detects the aberrations of the collimating lens , the Kepler telescope and of the phase plate .
By recording a reference measurement of the system without the phase plate first , the aberrations of the system ( spot reference ) can be subtracted to obtain the wavefront that carries only the aberrations of the phase plate .
Many applications make use of spatial filtering methods to reduce wave aberrations . To demonstrate the effect of spatial filtering on the transmitted wavefront , a pinhole with 100 µ m diameter can be inserted at the Fourier plane of the Kepler telescope , thereby low-pass filtering the wave generated by the phase plate ( the pinhole must be aligned in the x- , y- and z-axis by minimising wavefront rms ). The effect of this pinhole is small ; the corrected wavefront rms decreases from 0.1 µ m to 0.09 µ m . So the 100 µ m pinhole is replaced by a 50 µ m pinhole . The corrected wavefront rms distinctly decreases to 0.06 µ m . When replacing the 50 µ m pinhole with a 30 µ m pinhole , the corrected wavefront rms decreases further to 0.02 µ m . The PSF shown below is calculated from the corrected wavefront with an added refractive power representing the effect of the telescope lens with 40mm focal length .
The Optocraft wavefront sensors are distinguished by their high speed , single-shot measurements , excellent unreferenced accuracy , extreme dynamics and broad spectral ranges . They are also able to measure wavefronts with very strong higher order aberrations . They can measure large tilt angles and strongly defocused beams . They offer high intrinsic stability and reliability , powerful , customisable evaluation software and are versatile and flexible in usage . Optocraft ’ s systems are in operation in many demanding customer applications .
For more information on the SHSLab wavefront sensors from Micro-Epsilon , please visit www . micro-epsilon . co . uk or call the Micro-Epsilon sales department on + 44 ( 0 ) 151 355 6070 or emailinfo @ micro-epsilon . co . uk
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