Measurement of large aspheric surfaces by annular subaperture stitching interferometry

A new method for testing aspheric surfaces by annular subaperture stitching interferometry is introduced. It can test large-aperture and large-relative-aperture aspheric surfaces at high resolution,low cost,and high efficiency without auxiliary null optics.The basic principle of the method is described,the synthetical optimization stitching model and effective algorithm are established based on simultaneous least-square fitting.A hyperboloid with an aperture of 350 mm is tested by this method.The obtained peak-to-valley (PV) and root-mean-square (RMS) values of the surface error after stitching are 0.433λand 0.052λ(λis 632.8 nm),respectively.The reconstructed surface map is coincide with the entire surface map from null test,and the difference of PV and RMS errors between them are 0.031λand 0.005λ,respectively. This stitching model provides another quantitive method for testing large aspheric surfaces besides null compensation.     

Aspheric surface measurement based on sub-aperture stitching interferometry

In order to test convex aspheric surfaces without the aid of other null optics, a novel method combined sub-aperture stitching and interferometry called SSI （sub-aperture stitching interferometry） is introduced. In this letter, the theory, basic principle, and flow chart of SSI are researched. A synthetical optimization stitching mode and an effective stitching algorithm are established based on homogeneous coordinate＇s transformation and simultaneous least-squares fitting. The software of SSI is devised, and the prototype for testing of large aspheres by SSI is designed and developed. The experiment is carried out with five sub- apertures for a convex silicon carbide （SIC） aspheric mirror with a clear aperture of 130 ram. The peak-to- valley （PV） and root-mean-square （RMS） error are 0.186 λand 0.019 λ, respectively. For the comparison and validation, the TMA system which contained the convex asphere is tested by interferometry. The wavefront error of the central field of the optical system is 0.068 λRMS which approaches to diffraction limitation. The results conclude that this technique is feasible and accurate. It enables the non-null testing of aspheric surfaces especially for convex aspheres.     

Measurement accuracy verification of aspheric surface test with computer-generated hologram

A convex aspheric surface using a computer-generated hologram(CGH) test plate fabricated with novel techniques and equipment is tested.However,the measurement result is not verified via comparison with other methods.To verify the accuracy of the measurement,a perfect sphere surface is measured by the following.The measurement result is quantified into four parts:the figure error from the tested spherical surface;the figure error from the reference spherical surface;the error from the hologram;and the adjustment error from misalignment.The measurement result,removed from the later three errors,shows agreement to 4-nm RMS with the test by Zygo interfermeter of the same surface.Analysis of the CGH test showed the overall accuracy of the 4-nm RMS,with 3.9 nm from the test plate figure,0.5 nm from the hologram,and 0.74 nm from other sources,such as random vibration,various second order effects,and so on.Thus,the measurement accuracy using the proposed CGH could be very high.CGH can therefore be used to measure aspheric surfaces accurately.     

Measurement of a discontinuous object based on a dual-frequency grating

The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed: one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00~mm in height is simulated and a discontinuous object of ladder shape which is 32.00~mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.     

Nano-Traceability Study of a Cr Standard Grating Fabricated by Laser-Focused Atomic Deposition

A dimensional artifact is developed, which is a chromium （Cr） deposition grating fabricated by a laser-focused atomic deposition technique. The mean pitch of the grating is measured by using a metrological atomic force microscope with a large range, where a series of reference signs have been performed to locate the deposition area. Cosine error of the measurement result is analyzed and eliminated by the iterative angle calibration. The measurement result shows that the mean pitch of the grating is 212.66 ±0.02nm, which is very close to half of the standing laser wavelength （λ = 425.55 nm）. This means that the grating has traceability with high accuracy and can substitute the laser interference technology for instrument calibration. Moreover, using the Cr deposition grating as a nano standard can shorten the traceability chain and improve the practical application.     

A position sensor based on grating projection with spatial filtering and polarization modulation

A position sensor based on grating projection with spatial filtering and polarization modulation is presented. A grating is projected onto the object to be measured through a 4f optical system with a spatial filter. After reflected by the object, the grating projection is imaged on a detection grating through another 4f optical system to form moire fringes. The polarization modulated moire signal is detected to obtain the position information of the object. In the position sensor, the moire signal varies sinusoidally with the position of object. The measurement is independent of the incident intensity on the projection grating and the reflectivity of the object to be measured. In experiments, the effectiveness of the position sensor is proved, and the root mean square (RMS) error at each measurement position is less than 13 nm.     

Effect of crystalline lens surfaces and refractive index on image quality by model simulation analysis

The surfaces and refractive index of crystalline lens play an important role in the optical performance of human eye.On the basis of two eye models,which are widely applied at present,the effect of lens surfaces and its refractive index distribution on optical imaging is analyzed with the optical design software ZEMAX (Zemax Development Co.,San Diego,USA).The result shows that good image quality can be provided by the aspheric lens surfaces or (and) the gradient-index (GRIN) distribution.It has great potential in the design of intraocular lens (IOL).The eye models with an intraocular implantation are presented.     

Diffraction grating single-shot correlation system for measurement of picosecond laser pulses

We study and experimentally demonstrate a sensitive single-shot correlation system in which only a diffraction grating is used to produce a transverse time delay (TTD) in the reference pulse.The mechanism of the TTD introduced by the grating and the formation of the relative time delay (RTD) in the noncollinear correlation system are analyzed in detail.By using our system,we successfully measured the temporal duration of picosecond laser pulses,and a time resolution of ～0.047 ps is obtained at 1047 nm.The impact of the grating dispersion and the second harmonic beam walk-off effect on the measurement are considered.     

A plating method for metal coating of fiber Bragg grating

We present a method for metal coating optical fiber and in-fiber Bragg grating. The technology process which is based on electroless plating and electroplating method is described in detail. The fiber is firstly coated with a thin copper or nickel plate with electroless plating method. Then, a thicker nickel plate is coated on the surface of the conductive layer. Under the optimum conditions, the surfaces of chemical plating and electroplating coatings are all smooth and compact. There is no visible defect found in the cross-section. Using this two-step metallization method, the in-fiber Bragg grating can be well protected and its thermal sensitivity can be enhanced. After the metallization process, the fiber sensor is successfully embedded in the 42CrMo steel by brazing method. Thus a smart metal structure is achieved. The embedding results show that the plating method for metallization protection of in-fiber Bragg grating is effective.     

Design of a grating by a joint optimization method for a phase-shifting point diffraction interferometer

A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant. In order to measure the projection objective with a numerical aperture of 0.2, we present a joint optimization method of a pinhole and grating based on scalar diffraction and the finite difference time domain method. The grating constant and the film thickness are selected, and the duty cycle of the grating is optimized. The results show that in the grating processing the material chromium is adopted, the thickness is 200 nm, and the grating constant is 15 μm. When the duty cycle is 55%, the interference fringe contrast is the greatest. The feasibility of the design result is further verified by experiment.     

Fast and accurate measurement of large optical surfaces before polishing using a laser tracker

We present a method that accurately measures large optical surfaces before polishing using a laser tracker. Using the scanning mode of the laser tracker considerably improves measurement efficiency and minimizes the dominant errors caused by environmental change. We use this method to measure a φ1.3-m aspheric mirror and obtain a measurement uncertainty of 0.72 μm （root mean square, RMS）.     

Shape measurement of aspheric plastic lens with large angle

In this paper, according to the features of easy distortion and scratch for aspheric plastic lens, a noncontact measuring method is raised to test error in shape of the lens. Namely, the distance between a template and its image reflected with tested lens can be measured in nearly the vertical direction of the lens axis when the two-dimensional (2D) template is put near the measured surface. Then, the outline of the central cross-section could be obtained by calculating and curve fitting. Furthermore, three-dimensional (3D) surface can be imitated through rotating the component. A new fitting method of drift measurement is presented to prevent reducing precision when the lens and the template are fixed. The template is adjusted according to the position of the lens. The measurement precision is in the order of magnitued of sub-microns. Rotationally symmetric convex aspheric surface with any angle can be measured by this method.     

Compact FBG diaphragm accelerometer based on L-shaped rigid cantilever beam

A compact fiber Bragg grating(FBG) diaphragm accelerometer based on L-shaped rigid cantilever beam is proposed and experimentally demonstrated.The sensing system is based on the integration of a flat diaphragm and an L-shaped rigid cantilever beam.The FBG is pre-tensioned and the two side points are fixed,efficiently avoiding the unwanted chirp effect of grating.Dynamic vibration measurement shows that the proposed FBG diaphragm accelerometer provides a wide frequency response range(0-110 Hz) and an extremely high sensitivity(106.5 pm/g),indentifying it as a good candidate for embedding structural health monitoring and seismic wave measurement.     

Real-time measurement of the fast axis angle of a quarter-wave plate based on simultaneous phase shifting technique

Real-time measurement of the fast axis angle of a quarter-wave plate based on simultaneous phase shifting technique is presented.The simultaneous phase shifting function is realized by an orthogonal grating,a diaphragm,an analyzer array,and a 4-quadrant detector.The intensities of the light beams from the four analyzers with different azimuths are measured simultaneously.The fast axis angle of the quarter-wave plate is obtained through the four light intensity values.In this method,rotating elements are not required, so real-time measurement is achieved.     

A new phase-shifted long-period fiber grating for simultaneous measurement of torsion and temperature

A novel phase-shifted long-period fiber grating(PS-LPFG)for the simultaneous measurement of torsion and temperature is described and experimentally demonstrated.The PS-LPFG is fabricated by inserting a pretwisted structure into the long-period fiber grating(LPFG)written in single-mode fiber(SMF).Experimental results show that the torsion sensitivities of the two dips are?0.114 nm/(rad/m)and?0.069 nm/(rad/m)in the clockwise direction,and?0.087 nm/(rad/m)and?0.048 nm/(rad/m)in the counterclockwise direction,respectively.The temperature sensitivities of the two dips are 0.057 nm/℃ and 0.051 nm/℃,respectively.The two dips of the PS-LPFG exhibit different responses to torsion and temperature.Simultaneous measurement of torsion and temperature can be implemented using a sensor.The feasibility and stabilization of simultaneous torsion and temperature measurement have been confirmed,and hence this novel PS-LPFG demonstrates potential for fiber sensing and engineering applications.     

Efficiency measurement of optical components in 45-110 nm range at beamline U27,HLS

We propose a general correction method for the efficiency measurement of optical components in the 45-110 nm range to eliminate the contamination of higher-order harmonics at beamline U27 of the Hefei Light Source (HLS). The influence of harmonics can be deducted effiectively from the initial measurement results through the analysis of the proportion of harmonics with a transmission grating and the efficiency measurement of optical elements at the harmonics wavelengths. The reflectivity measurement of a gold film is performed at the beamline to verify its validity. Results indicate that the corrected reflectivity is in good agreement with the theoretical value. The maximal deviation amounts to 1.93% at a wavelength of 85 nm and an incident angle of 5°.     

Laser-induced damage on large-aperture fused silica gratings

Two sets of laser-damage experiments on large-aperture fused silica optics have been carried out in a high-power laser facility. Severe damage has been found on the grating which presented dense craters on the front surface. This phenomenon is quite different from other fused silica optics, which are damaged on the rear surface. The damage possibility due to the redeposition layer was ruled out by acid-etching the grating’s front surface. The remarkable stimulated Brillouin scattering (SBS) effect was observed in grating and the reason for the front surface damage is thought to be the backward SBS.     

Stimulated Brillouin Scattering Damage of Large-Aperture Fused Silica Grating

Laser induced damage experiment is carried out on a large aperture laser facility. Severe damage is observed on a large-aperture fused silica grating which presents dense craters on the front surface and six cracks alternatively located at the front and the rear surface. The bizarre fact about the damage on the grating is that, unlike other optics, the damage craters are almost on the front surface. According to observation, damage phenomenon is due to the stimulated Brillouin scattering （SBS） effect occurring in the grating, which includes the transverse SBS, the back SBS and the zigzag SBS.