Wavefront error measurement of high-numerical-apertureoptics with a Shack–Hartmann sensor and a point source

Jin-Seok Lee, Ho-Soon Yang, and Jae-Won Hahn

We developed a new, to the best of our knowledge, test method to measure the wavefront error of thehigh-NA optics that is used to read the information on the high-capacity optical data storage devices.The main components are a pinhole point source and a Shack–Hartmann sensor. A pinhole generates thehigh-NA reference spherical wave, and a Shack–Hartmann sensor constructs the wavefront error of thetarget optics. Due to simplicity of the setup, it is easy to use several different wavelengths without significantchanges of the optical elements in the test setup. To reduce the systematic errors in the system, a simplecalibration method was developed. In this manner, we could measure the wavefront error of the NA 0.9objective with the repeatability of 0.003� rms �� � 632.8 nm� and the accuracy of 0.01� rms. © 2007Optical Society of America

OCIS codes: 120.3930, 120.5050, 010.7350, 220.4840.

1. Introduction

There have been rapidly increasing demands onsmall but high-capacity optical data storage devicesdue to the growing archive and backup requirements.The density of the optical disk is increased as a NAof the objective lens is higher, or the wavelength isshorter. For example, the compact disk uses NA 0.45optics at 780 nm for 650 Mbytes of data storage andthe digital video disk uses NA 0.6 optics at 650 nm for4.7 Gbytes. From 2003, the new data storage devicecalled the Blu-ray disk has been commercialized formore than 23 Gbytes of data storage, which can con-tain 2 h of digital high-definition video or 13 h ofstandard broadcast. This device uses a high-NA op-tics of 0.85 at 405 nm of wavelength. Also, severalother research studies are still being carried out forhigher data storage. For example, for 100 Gbytes read-only memory (ROM) disk, the high-density near-fieldoptical recording system that uses a 405 nm laserwavelength and a NA of 1.84 has been reported.1

This high-NA optics has a near diffraction-limitedperformance so that it is essential to test the opticsbefore using it. One way to test the high-NA optics isto measure the wavefront error (WFE). The rms WFEof the diffraction-limited optical system is 0.07� rms,according to Rayleigh criteria. However, it has beenrare to talk about the WFE of a high-NA optics. Themain reason would be that it is very difficult to gen-erate the high-NA reference wavefront by a conven-tional transmission sphere used in commercial phaseshifting interferometers (PSI).

In this situation, the point-diffraction interferom-eter2 (PDI) may be a promising candidate for theWFE measurement of high-NA optics because thehigh-NA spherical wave can simply be obtained byusing a small pinhole. It is a rule of thumb that thediameter of a pinhole is 0.5��NA for a wavelength �and a NA. For example, the pinhole of 110 nm indiameter can produce the NA 1.84 spherical waveat a 405 nm wavelength according to this rule ofthumb. Several researchers have demonstrated thatthe wavefront from a pinhole is a near-ideal sphericalwave.3–5 However, the conventional PDI or phase-shifting point-diffraction interferometer6 (PS�PDI)has been used for low NA optics because of featuresize limitation in the point-diffraction device, eventhough some researchers developed a special PDI tomeasure the NA 0.8 optics.7

In the research described below, we developed anew, to the best of our knowledge, method to measurethe transmitted WFE of the high-NA optics by usinga Shack–Hartmann (SH) sensor as a wavefront sens-

J.-S. Lee ( jsrace@yonsei.ac.kr) and J.-W. Hahn ( jaewhahn@yonsei.ac.kr) are with the School of Mechanical Engineering,Yonsei University, Seoul, Korea. H.-S. Yang is with the KoreaResearch Institute of Standards and Science, Daejeon, Korea.

Received 11 August 2006; revised 25 October 2006; accepted 26October 2006; posted 27 October 2006 (Doc. ID 73977); published 1March 2007.

0003-6935/07/091411-05$15.00/0© 2007 Optical Society of America

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ing instrument and a pinhole to generate the refer-ence spherical wave. The SH sensor has been widelyused for the optical testing.8–14 It has a wide dynamicrange, insensitivity to vibration, and simplicity of thesystem. Also, it does not need to use significant effortto make a good fringe visibility, as in the PDI orPS�PDI. Furthermore, due to its simplicity, it canaccurately measure the WFE of optics at several dif-ferent wavelengths just with some relatively simplecalibration method, while the conventional inter-ferometer needs to modify its optical components sig-nificantly depending on the wavelength used. Theseadvantages have made the SH sensor a promisingalternative for the interferometer in many applica-tions.

In Section 2, the test method for the high-NA opticsis described, and the calibration process related to thesystematic errors in the test setup is explained inSection 3. Some experimental results with the NA 0.9objective are shown in Section 4.

2. Test Setup

Figure 1 shows the schematic test setup for the WFEmeasurement of high-NA optics. The primary lightsource is a 632.8 nm He–Ne laser that can easily bereplaced with another light source such as a 405 nmlaser diode because of the coupling of the laser andsingle-mode fiber. The laser is linearly polarized. Thebeam after fiber is focused onto the pinhole with thefocusing lens. The pinhole generates the near-perfectspherical reference wavefront without the need ofany optics. The beam passing through the test lensare imaged on the SH senor by relay optics that con-sists of two doublets. The magnification of relay op-tics is 1.7.

The SH sensor used in this research is a commer-cially available unit. It has a 37 � 37 array of micro-lenses of which the diameter is 198 �m, and the focallength is 15.483 mm. The microlens array is placed infront of a CCD, which has a 1004 � 1004 pixel array,and its pixel size is 7.4 �m � 7.4 �m. This SH sensorhas its aperture of 7.4 mm � 7.4 mm and can operateat a bandwidth of 300–1100 nm.

To measure the NA 0.9 optics, we prepared twopinholes, 300 nm in diameter for the 632.8 nm wave-length and 200 nm in diameter for 405 nm accordingto a rule of thumb explained in Section 1. The pin-holes are fabricated on the 200 nm thick Ag films,which are coated on the glass substrate with ion-assisted evaporation process, with focused ion-beam

equipment. Figure 2 shows the scanning electron mi-croscopy (SEM) image of the 300 nm pinhole. Thesize of pinhole is 353 nm in long axis and 345 nm inshort axis, which shows a good circularity. Accordingto Goldberg et al.,4 this pinhole can generate thediffracted spherical wavefront of which the peak-to-valley (PV) error is within 0.13 nm. The linear polar-ization of the beam does not significantly affect thequality of diffractive spherical wavefront. Accordingto Sekine et al.3 the PV WFE of a spherical wavefrontafter an elliptical pinhole (length of each axis variedfrom 30 to 60 nm) was within 0.01� �� � 13.5 nm�even with a linear polarized input beam. As for the200 nm pinhole, its size was 222 and 216 nm in longand short axes, respectively, which qualifies to gen-erate the spherical wave to test the NA 0.9 optics at405 nm wavelength.

3. Calibration Method

This test setup has two kinds of error sources to beovercome for the accurate measurement; errors in theSH sensor and aberrations generated by relay optics.To reduce the effects of errors, it is necessary to cal-ibrate the test setup. As a calibration method, weused the high-quality reference lenses of which theWFE is 0.01� rms �� � 632.8 nm�, measured by aZYGO interferometer (model GPI-XP). The referencelens has the low NA of 0.1 so that there is no signif-icant misalignment error when measuring it with the

Fig. 1. Test setup for measuring transmitted wavefront aberration of high-NA optics.

Fig. 2. SEM image of the 300 nm pinhole.

1412 APPLIED OPTICS � Vol. 46, No. 9 � 20 March 2007

ZYGO interferometer. This reference lens replacedtarget optics in Fig. 1, and the measurement wascarried out at 632.8 nm wavelength. If the differentwavelength is used, another reference lens that has ahigh quality at that wavelength needs to be prepared.These measurement data were stored as a referencefile. These reference data include all kinds of errors ofthe test method, including aberrations from relay op-tics, nonuniformity of the lens array of the SH sensor,and the centroid error due to the pupil irradianceprofile generated by a polarized laser beam. There-fore, the measurement of the target optics with re-spect to this reference data is absent from the errorsources. Figures 3(a) and 3(b) show the WFE maps ofthe reference lens before and after the calibrationprocess. The WFE of the reference lens is 0.031� rms�� � 632.8 nm� before the calibration; however, it isreduced to 0.003� rms after using it as a referencefile. The main source of the residual error is thoughtto be the electrical noise of the detector. Obviously,this error does not mean the measurement uncer-tainty because the reference data include the WFE of

reference lens, which is significant compared with theresidual WFE after the calibration. In this calibrationmethod, the quality of the reference lens is the majorlimitation of the measurement accuracy. Nevertheless,the high-quality reference lens and small residual er-ror make it possible to measure the WFE of the targetoptics with the diffraction-limited performance.

4. Measurements of the Numerical Aperture0.9 Objective

To verify the capability of measuring the high-NAoptics, we measured NA 0.9 microscope objective lensfrom Nikon Company (BD Plan Apochromat 81838),using the method suggested in this paper. The work-ing distance and the exit pupil size of this objectiveare �400 �m and 3.4 mm, respectively. This exit pu-pil is expanded by 1.7� image relay optics to fill thesensing area of SH sensor. The relay optics and SHsensor were calibrated by the procedure explained inSection 3. Figure 4 shows the WFE of NA 0.9 objec-tive at two different wavelengths, 632.8 and 405 nm.

Fig. 3. WFE of the high-quality reference in the test setup (a) be-fore the calibration and (b) after the calibration.

Fig. 4. WFE of NA 0.9 objective lens (a) at � � 632.8 nm and (b) at� � 405 nm.

20 March 2007 � Vol. 46, No. 9 � APPLIED OPTICS 1413

The different pinholes were used for each wave-length: 300 nm pinhole for the 632.8 nm wavelengthand 200 nm pinhole for 405 nm. However, the samecalibration processes were carried out in both casesbefore the measurement of the objective. The analysissoftware calculated the WFE by modal methods.15

The high-NA optics is sensitive to the alignment, es-pecially to the lateral shift. Therefore, the pinholepoint source and test optics should be aligned pre-cisely. For this, the test optics was aligned until weobtained the minimum value of coma and the sym-metric intensity distribution. The rms WFEs of theobjective were 39.9 nm for the 632.8 nm wavelengthand 52.3 nm for 405 nm wavelength. This small dif-ference means that the microscope objective used inthis measurement was well made to correct the chro-matic aberration, which is compliant to the specifica-tion of the product. Also, this experiment shows theflexibility in the test wavelength; without a signifi-cant change of the optical components in the testsetup, we could measure the optics at two distinctivewavelengths.

To estimate the measurement uncertainty of thetest method, the same objective was measured tentimes repeatedly at the 632.8 nm wavelength. EachWFE was fitted to 36 Zernike circular polynomialsaccording to the Born and Wolf representation.16 Thestandard deviation (SD) of the rms WFE of repeatedmeasurements is 0.003� �1��, which is exactly thesame as the residual WFE explained in Section 3.This means that the variation of the measurement ismainly from the detector electrical noise. Figure 5shows the averaged aberration polynomial coeffi-cients and the SD of each coefficient. These variationsof each coefficient imply the limit of the measurementrepeatability of the test setup.

Figure 6 shows the polynomial coefficients mea-sured at two different axial rotation orientations, 0°and 180°. Particularly, the signs of coefficients re-lated to the axial rotation (7th–10th, 16th–21th, and29th–36th terms) in the 180° rotation measurement

data were reversed to make it easy for the comparisonof two measurements. It is not clear whether theaberration measured follows the axial rotation of thetest optics because of the fluctuation of the coeffi-cients. Actually, the fluctuations of each coefficientare within the variation of the repeated measure-ments shown in Fig. 5, which means that there are nosignificant systematic errors in the test setup. It isclear from experiments above that this test methodcan measure the WFE of the high-NA optics withdiffraction limited performance with the repeatabil-ity of 0.003� rms �� � 632.8 nm�.

5. Concluding Remarks

In this paper, we explained the new test method tomeasure the high-NA optics, using a SH sensor as aWFE sensing instrument and a pinhole to generatethe high-quality reference spherical wave. After theproper calibration process, this test setup could mea-sure the NA 0.9 objective with the repeatability of0.003� rms �� � 632.8 nm� and the accuracy of 0.01�rms. This accuracy was dependent on the quality ofthe reference lens used in the calibration. If we usethe higher quality of reference lens, then we would beable to measure the target optics with higher accu-racy. This test method also made it easy to use severaldifferent wavelengths without significant changes ofthe optical elements in the test setup. Therefore, thismethod is quite useful in measuring the high-NA op-tics in terms of generation of the high-NA referencewave and flexibility in the usable wavelength.

To measure even higher NA optics in this manner,there are at least two obstacles to overcome; lighttransmission and quality of spherical wave. In themeasurement of the NA 0.9 objective, the light trans-mission through the pinhole of 300 nm diameter wasenough to align the test optics and measure the WFEusing a CCD of SH sensor. However, if we reduce thediameter of pinhole to measure higher NA optics, thelow light transmission would be a serious problem. Toget around this problem, the high-power light source

Fig. 5. Magnitude of coefficients of Zernike circular polynomials.Each point is the averaged value after ten repeatability measure-ments of NA 0.9 objective.

Fig. 6. Measurements of NA 0.9 objective lens at 632.8 nm wave-length at two different axially rotation orientation (Born and Wolfrepresentation was used).

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or high-performance cooling CCD might be helpful.Another critical problem is that as the NA of optics ishigher, the working distance is decreased, even in theregion of Fresnel diffraction. That means that thewavefront from the pinhole may not be an idealspherical. In this case, the quite different calibrationprocess may be needed to compensate the distortedwave from the pinhole. The limitation on the NAmeasurable using the method explained in this paperneeds to be investigated further.

This work was supported by the Korea Sci-ence and Engineering Foundation through projectsM10609000019-06M0900-01910 and M10400000313-05J0000-31310.

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