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Dual-wavelength interferometry (DWI) could extend the measured range of each single-wavelength interferometry. The synchronization of the two working wavelengths in DWI is of high efficient, and the generated moire fringe indirectly represents the information of the measured long synthetic-wavelength (λS) phase. However, the extraction of the measured synthetic-wavelength phase is rather arduous from the moire fringe. To retrieve the synthetic-wavelength phase from the moire fringe patterns, we present a carrier squeezing dual-wavelength interferometry method (CSDI) in simultaneous DWI (SDWI). After the mathematical square of the moire fringe patterns, the multiplicative moire phase-shift fringe patterns with π/2 phase shift at λS are combined into a single spatial-temporal fringe (STF). By converting the temporal phase shift into spatial carrier and the introduction of the carrier, the measured synthetic wavelength phase is retrieved by the filter and inverse Fourier transform of the STF spectrum. Compared with other methods, CSDI method could suppress the influence of the phase-shift error and only requires 4 frame phase-shift interferograms. Numerical simulations are executed to demonstrate the performance of the CSDI method in SDWI with the peak-to-valley (PV) value of 1.46 nm and the root mean square (RMS) values of 0.23 nm for the demodulated error. And the precision is better than PV of 20 nm (0.0059λs) and RMS of 6 nm (0.0017λs) even when the distribution range of the phase-shift error is as high as ± 10% relative to the π/2 phase shift step at λS. Finally, our experimental results indicate that the measurement accuracy is better than 1.3% for a step with the height of 7.8 µm, and 0.5% for the step height of 6.233 µm for a Fresnel lens.

Dual-wavelength interferometry could extend the measured range of single-wavelength interferometry by combining the two single wavelength phases, particularly for the measurement of step height. When testing the high-reflectivity surfaces with the single wavelength Fizeau interferometer, we have presented the π ∕ 4 phase-shift carrier squeezing interferometry (QCSI) method for phase extraction with multi-beam interference ( Appl. Opt . 55, 1920–1928, 2016). In this paper, we propose an integer and decimal portions synthetization (IDS) method for the multi-beam interference in the dual-wavelength Fizeau interferometer. One of the single wavelength wrapped phases is demodulated by the multi-beam interference QCSI algorithm, while the second of the single wavelength wrapped phases is extracted by the conventional two-beam interference phase-shift algorithm, so the equivalent wavelength unwrapped phase is derived from the two single wavelength wrapped phase. The decimal portion of synthesized phase is then obtained directly from the first single wavelength wrapped phase, and the integer portion of synthesized phase is obtained from the fringe order of the first single wavelength wrapped phase determined by the equivalent wavelength unwrapped phase. The proposed non-iterative IDS method avoids the common error magnification effect in the two-wavelength techniques, and only requires no more than 8 frame phase-shift interferograms for each single wavelength. Its robust performance is validated by both simulations and experiments in the presence of multi-beam interference as well as phase-shift error for measuring objects with height discontinuities.

The ideal mapping geometry in a Fizeau interferometer is to map equal height increments on a flat object and equal angle increments on a spherical surface to equal heights on the detector. So the initial intent of the optical design of Fizeau transmission spheres (TSs) is to provide R‐θ mapping geometry for equal angle increments. The corresponding unequal heights mapping will introduce retrace error as coma when linear carrier fringes exist. On the contrary, equal heights mapping with R‐sin θ mapping geometry will avoid linear carrier fringes induced coma error. These two different mapping geometries conflict especially for the TS with a small f-number. In this paper, we will first explore the design and the performance of the f/0.75 TS according to the two different mapping geometries, and then evaluate the mapping geometry for the commercial ZYGO f/0.75 TS, and give some engineering notes for the designers, the metrologists, and the fabricators in the optical laboratory.

The peach fruit borer Carposina sasakii Matsumura(Lepidoptera: Carposinidae)(= Carposina niponensis(Walsingham)) is a harmful and widespread pest insect that attacks many types of fruit,including apple,peach and jujube,in northern China.Among these hosts,jujube has been most severely affected,with about 90% of Chinese jujube orchards being damaged.The larvae drill into the fruit and eat the pulp and kernel,producing bore dust and frass that make the fruits inedible by humans,and causing the fruit to fall from the trees.The quality and quantity of fruits affected by the borer are markedly reduced,as are the yields of infested orchards,causing large economic losses.The peach fruit borer is predominantly found in Asian countries(China,Japan,Korea) and the far east of Russia.Because of the risk to fruit orchards,in 1988 the European and Mediterranean Plant Protection Organization placed C.sasakii on the A1 list of pests recommended for control by quarantine.However,the peach fruit borer is difficult to control because it is concealed within the fruit,and general methods of pest treatment fail to achieve sustainable control.It has therefore become necessary to identify and utilize natural enemies of this pest to develop a bio-control strategy.Many researchers have worked on this problem,and have obtained valuable data and results.However,there are many factors that remain to be elucidated;for example,precisely which species are parasitoids of the peach fruit borers that attack the jujube tree,how are they restricted to their host,and what is the host-parasitoid relationship? In this project,we investigated populations of parasitic wasps attacking C.sasakii in jujube orchards in Shaanxi,Shanxi and Henan provinces and in Ningxia Hui Autonomous Region in 2009—2010.Three species of parasitic wasp were identified(Pristomerus chinensis Ashmead,Chelonus(Microchelonus) zhangi Zhang and a species of Pteromalidae) and all were reared from their host cocoons.P.chinensis Ashmead and C.(M.) zhangi Zhang are both preponderant agents,but their population size varied markedly among the above four regions;P.chinensis was found predominantly in Shaanxi and Shanxi provinces,whereas C.(M.) zhangi was observed principally in Henan.The relationship between emergence,parasitism rate and host were studied for P.chinensis and C.(M.) zhangi.The results indicate that P.chinensis emerged half a month later than its host.Adult hosts emerged from over-winter cocoons in the middle of June,with a parasitism rate of 8.86%;the summer generation emerged from the last week of August to the first week of September,with a 25% parasitism rate.For C.(M.) zhangi,the summer generation emerged from the middle of August to the first week of September.In general,fruit drop occurred in the first(in 2010) to the second(in 2009) week of August in jujube orchards in Puyang city,Henan province;C.(M.) zhangi began to emerge one week later,with the peak emergence at 10—12 days.The graph of parasitism rate for C.(M.) zhangi revealed three time periods: from 16 to 26 August,from 27 to 31 August and from 1 to 8 September.As a whole,the parasitism rate declined from the first period to the third,which could be related to host behavior.No insecticide was used in the experimental areas during the years 2009—2010;as a consequence,the parasitism rate for C.(M.) zhangi increased markedly to 64.52% in 2010.Thus,it can be seen that local natural enemies have been playing an important role in controlling the peach fruit borer naturally,and should be protected and utilized appropriately.