Figure 1 presents a schematic of the proposed pro-grammable light spectrum synthesis system. In this optical arrangement, the white-light source is trans-mitted through a single-mode fiber (SMF), and the light emerging from the optical collimator is dif-fracted by a grating. The⫺1-order diffractive light is incident on the DMD chip, where its reflective direc-tion is governed by the direcdirec-tion of the micromirrors on the chip’s surface. In general, the micromirrors on a DMD chip have two ON–OFF bistable states (i.e., 12° and ⫺12°, respectively), which control the inci-dent light such that it is reflected from the DMD surface in one of two different reflective directions.3 In the present configuration, the⫺12° state reflective light is collected and focused on the fiber lens through an arrangement of biconvex and biconcave lenses.
The spectrum synthesis results are then obtained using an optical spectrum analyzer (OSA).
The collimated light incident on the grating is dif-fracted according to the following formula:
n ⫽ d共sin d⫺ sin i兲, (1) where n is the order of diffraction, d is the grating period, is the wavelength, dis the diffraction angle, andiis the incident angle with respect to the normal axis of the grating. As shown in Fig. 1, the⫺1-order
diffracted light is incident on the DMD chip with an angle of cen with respect to the central wavelength 共cen兲. Therefore the diffractive spread angle, ⌬, from the grating is expressed as
⌬ ⫽ max⫺ min
⫽ sin⫺1共⫺max兾d ⫹ sin i兲
⫺ sin⫺1共⫺min兾d ⫹ sin i兲, (2) wheremax andmin are the⫺1-order diffractive an-gles with respect to the maxima wavelength, max, and the minima wavelengthmin.
Figure 2 illustrates the spectral distribution of the diffracted light incident on the DMD chip. The spectral spread length, Lx, at the DMD chip along the diffrac-tive direction (i.e., the X-axis direction) is given by
Lx⬵ D ⫻ ⌬兾sin t, (3) where D is the distance from the grating to the DMD chip andtis the DMD tilt angle with respect to the diffracted light axis. In the orthogonal direction (i.e., the Y-axis direction), since an assumption is made that the beam propagates in parallel, the spread length can be expressed as
Ly⬵ w, (4)
where w is the light beam waist after it exits the fiber collimator. Therefore the X axis corresponds to the spectral distribution and the Y axis to the intensity distribution. From the above, the DMD chip mi-cromirror resolution of wavelength R is given by
R⫽ 共max⫺ min兲兾共Lx兾p兲, (5) where p is one pixel side length, such that共Lx兾p兲 gives the total number of pixels in the X-axis direction. The micromirrors on the DMD chip reflect the diffracted light in two different directions because they each have two ⫾12° states, which are controlled by the DMD pattern. When the micromirror state is set to
⫺12° (i.e., the OFF state), the diffracted light from
Fig. 1. Schematic of spectrum synthesis system.
Fig. 2. (Color online) Diffracted light incident on a DMD chip.
10 November 2006兾 Vol. 45, No. 32 兾 APPLIED OPTICS 8309
this particular pixel is collected by the fiber lens as illustrated in Fig. 1. Therefore a synthesized spec-trum can be obtained by adjusting the pattern of the DMD chip where the diffraction light is incident.
B. Digital Micromirror Device Chip Scanning Calibration If all of the micromirrors on the DMD chip are set to
⫺12°, all of the ⫺1-order diffracted light on the DMD chip is reflected into the fiber lens. To calibrate the relationship between the diffraction wavelength and the X-axis coordinates of the DMD chip, a string-line pattern is scanned along the X-axis direction. Simi-larly, the diffraction intensity is calibrated by scan-ning a string-line pattern along the Y-axis direction.
Figure 3 illustrates both string-line pattern scans along the X and Y axes in the DMD chip. The spec-trum corresponding to an individual DMD pixel is expressed as
F共s, i兲 ⫽ D共xm, yn兲, (6) where F共s, i兲 is the calibrated light spectrum, s is the spectrum, i is the intensity, and D共xm, yn兲 are the DMD pixel coordinates. If the spectrum on the DMD chip has a Gaussian10or uniform distribution, the inten-sity distribution along the Y axis is easily obtained.
However, these conditions do not always hold. There-fore string-line pixel scans are performed along the X and Y axes, respectively, to obtain the two-dimensional spectrum distribution on the DMD chip.
From Eq. (6), the light spectrum synthesis principle is given by
S共s, i兲 ⫽兺关D共xm, yn兲␦共xm, yn兲兴, (7) where S共s, i兲 is the synthesized light spectrum and
␦共xm, yn兲 is the ON–OFF state of the DMD pixels.
When the micromirror state is ⫺12° (i.e., the ON state),␦共xm, yn兲 ⫽ 1; otherwise ␦共xm, yn兲 ⫽ 0.
3. ZEMAX Simulation of the Light Spectrum Synthesis System
Figure 4 presents a schematic of the light spectrum synthesis system simulated using the ZEMAX optical design software. Since in ZEMAX, the light source
cannot be specified as a continuous spectrum, this study specified a light source with an infrared C-band Gaussian spectrum distribution with three different wavelengths, i.e., min ⫽ 1530 nm, cen ⫽ 1550 nm, and max ⫽ 1565 nm. The simulations assumed the following: (i) a collimated light beam waist of w⫽ 1 mm, (ii) a telecommunication grating with a grating period of 1.667m, (iii) a light diffracted or-der of ⫺1, and (iv) an incident angle of i ⫽ 45°.
Therefore from Eqs. (1) and (2), respectively, it was found that the⫺1-order diffracted angle was cen ⫽
⫺12.879° and the spread angle was ⌬ ⫽ 1.235°. The distance between the grating and the DMD chip, D, was set at 250 mm. As shown in Fig. 4, lenses L1, L2, and L3 focused the⫺12° state diffracted light from the DMD into the fiber lens. The system parameters analyzed by the ZEMAX simulations were then used to establish an experimental setup for a digital pro-grammable light spectrum synthesis system.
Figure 5 presents an enlarged view of the DMD chip shown in Fig. 4. As shown, the chip is tilted at an angle of 57° about the light axis. As discussed previ-ously, the micromirrors on the DMD chip have⫾12°
states. In the present simulations, the micromirrors at either end of the DMD chip were set to ⫺12°
(i.e., the OFF state), causing the incident light to be reflected through an angle of 90°. Meanwhile, the micromirrors in the central region of the DMD were set to the 12° state (i.e., the ON state), causing the incident light to be reflected at an angle of 42°. From Eqs. (3) and (4), respectively, the X-axis spread length was found to be Lx⫽ 6.425 mm and the Y-axis spread length to be w⫽ 1 mm.
4. Experimental Setup and Calibration
A. Experimental Setup
The light source in the present experiments was an amplified spontaneous emission (ASE) from an
Fig. 3. String-line pattern scans along the X and Y axes of a DMD chip.
Fig. 4. (Color online) ZEMAX simulation of the light spectrum synthesis system.
EDFA with a center wavelength of cen ⫽ 1550 nm and a spectral bandwidth of⌬ ⫽ 37 nm. As shown in Fig. 6, the light source has two peaks and therefore does not conform to a simple Gaussian distribution.
Figure 7 presents a photograph of the experimental setup of the light spectrum synthesis system de-signed in accordance with the ZEMAX simulation results. The current optical arrangement used an Op-tometrics LLC telecommunication grating (catalog no. 3-4616) with a period of 1.667m and a blaze angle of 28°41’. The typical efficiency of this grating for a wavelength of 1550 nm is approximately 80%.
From Rayleigh’s criterion, the grating’s resolution limit was calculated to be 1.826 nm atcen. The DMD chip controller module (PSI Discovery 1100 starter kit) in the experimental setup used a Texas Instru-ments 0.7 in. (1 in. ⫽ 2.54 cm) infrared DMD chip consisting of a 1024 horizontal⫻ 768 vertical array of aluminum micromechanical mirrors with a transi-tion time of 20s arranged with a pitch of 13.68 m.
The patterns on the DMD chip were manipulated using graphical user interface software (Version 1.3) and a USB interface. The frame rate of the DMD chip
was 100 frames兾s with a standard USB 2.0 interface, but was improved to 4000 frames兾s using an accel-erative board. Focusing lenses L1 and L2 (see Fig. 4) were biconvex spherical lenses with focal lengths of 100 and 50 mm, respectively. Meanwhile, L3 was a biconcave spherical lens with a focal length of ⫺50 mm. The fiber lens (LPF-05-1550-9, OZ Optics Ltd.) had a focal length of 1.99 mm and a working distance of 1.5 mm. The OSA is an HP 70952B and its reso-lution is 0.065 nm⫾ 15% at FWHM.
B. Calibration of the Light Spectrum Synthesis System Figure 8 presents the light spectrum collected by the fiber lens when all of the micromirrors on the DMD chip are set to the⫺12° state.
In the calibration process, DMD string-line pat-terns are scanned step by step along the X axis, as shown in Fig. 3. Each string-line pattern consists of 30 micromirror columns. If too few micromirror col-umns are included within the string-line pattern, a serious diffraction effect is induced because the col-umn pattern resembles a single slit. Conversely, if too
Fig. 5. Enlarged view of a DMD chip region of the light spectrum synthesis system.
Fig. 6. ASE spectrum from EDFA.
Fig. 7. (Color online) Experimental setup of the light spectrum synthesis system.
Fig. 8. DMD reflected light spectrum captured by a fiber lens.
10 November 2006兾 Vol. 45, No. 32 兾 APPLIED OPTICS 8311
many micromirror columns are included, the resolu-tion will be poor. Figure 9 illustrates the relaresolu-tionship between the diffracted light wavelength and the DMD X-axis pixel coordinates as obtained by X-axis string-line pattern scanning. From Eq. (5), the DMD chip wavelength resolution R is found to be 0.076 nm兾pixel.
Since the spread of the light diffracted in the Y-axis direction is narrow [from Eq. (4), Ly⫽ w ⫽ 1 mm], the scan period must be shorter than that used for the X-axis scanning to enhance the intensity resolution.
A 10-pixel共136.8 m兲 string-line pattern was found to induce a serious diffraction effect, and hence scan-ning was performed using a string-line pattern with an average value of 30 pixels. For example, the in-tensity in row 45 represents the average recorded intensity over rows 31 to 60 (i.e., 30 pixels in total).
Although the measured values of intensity therefore indicate the relative intensity rather than the abso-lute intensity, the results nevertheless provide a good indication of the actual intensity. The relationships between the DMD micromirror coordinates and the wavelength and intensity, respectively, were used to draw the contour of F共s, i兲 ⫽ D共xm, yn兲 as illustrated in Fig. 10. It can be seen that the contour has two peaks, i.e., at 1545 and 1534 nm, respectively, as expected from Fig. 8. Furthermore, the results of Lx ⫽ 450 pixels ⫻ 13.68 m ⫽ 6.156 mm and Ly⫽ 90 pixels ⫻ 13.68 m ⫽ 1.23 mm are consistent
with the results presented in Section 3. The area shown in Fig. 10 contains 40,500 pixels, i.e., just 1兾20 of the total number of pixels on the DMD chip. Hence the potential exists to design a multichannel system.
Finally, the contour can be used to synthesize differ-ent spectra by applying Eq. (7). Four light spectrum synthesis examples are presented for illustration purposes in the following section.
5. Illustrative Examples of Synthesized Spectra and Discussion
Figure 11(a) shows a square spectrum profile synthe-sized by the calibration pattern presented in Fig. 10.
It can be seen that the spectrum is poorly defined because the 30-pixel string-line scanning pattern is not sufficiently precise. However, the DMD pattern can be simply and quickly tuned according to the contour shown in Fig. 10. The wavelength and inten-sity of the synthesis spectrum in Fig. 11(a) need to be checked and then the numbers of the DMD
OFF-Fig. 11. Synthesis of square spectrum profile: (a) initial profile and (b) profile following the DMD pattern adjustment.
Fig. 9. Relationship between the diffracted light wavelength and DMD X-axis pixel coordinates.
Fig. 10. Contour of diffracted light incident on a DMD chip.
state pixel can be slightly added or subtracted accord-ing to Fig. 10 until the spectrum becomes Fig. 11(b).
Figure 11(b) shows the square spectrum profile fol-lowing an adjustment of the DMD pattern. It is apparent that the flatness of the profile is greatly improved. Note that the edge of the synthesized spec-trum can be improved by increasing the grating res-olution.
Figure 12 shows the synthesis results obtained for a sawtooth spectrum profile [Fig. 12(a)] and a trian-gular spectrum profile [Fig. 12(b)]. It can be seen that the original synthesized spectra obtained using the calibration contour in Fig. 10 must be corrected by adjusting the DMD chip pattern. As in the example presented in Fig. 11, not only the spectrum but also the intensity corresponding to each pixel must be manipulated.
The methodology that we discuss above can be ap-plied to a rapid programmable tunable light source by exploiting the relationship between the pixel coordi-nates and the wavelength. Since the spectrum in a
programmable tunable light source has a simple syn-thesized Gaussian distribution, the calibration rela-tionship in Fig. 9 is sufficient. Figure 13 shows an example of a programmable tunable light source with three center wavelengths, i.e., 1531.50, 1542.00, and 1552.25 nm, where each wavelength has a band-width of approximately 3.8 nm.
From above, the wavelength bandwidth in the sys-tem could be narrowed by using a proper grating and optical design, for example, increasing the grating resolution, increasing the distance D (as illustrated in Fig. 1), or reducing the scanning DMD pixel num-ber. However, the diffractive effect should be consid-ered when fewer scanning DMD pixel numbers are applied.
In general, the results presented in Figs. 11–13 indicate that a spectrum with a Gaussian distribu-tion (as illustrated in Fig. 13) can be synthesized simply by applying the calibration relationship illus-trated in Fig. 9. However, if synthesizing the spec-trum involves manipulating not only the specspec-trum wavelength but also the intensity, the calibration contour in Fig. 10 must be applied. Due to the lower resolution of the intensity distribution calibration, a further correction of the DMD chip pattern is also required.
6. Conclusions
This study has applied the results obtained from the ZEMAX optical design software to develop a digital programmable light spectrum synthesis system based on the digital micromirror device chip from Texas In-struments. It has been shown that this chip provides a wavelength resolution of 0.076 nm兾pixel. In contrast to the spectrum synthesis system presented in Ref. 10, the current approach does not insist that the light source spectrum must have a Gaussian distribution.
The two-dimensional spectral and intensity distribu-tion of the spectral profile is calibrated by scanning X-and Y-string-line patterns across the light spot on the DMD. Any spectral profile can then be synthesized by applying the relationship between the spectrum and
Fig. 12. DMD programmable spectral profile synthesis results:
(a) sawtooth profile and (b) triangular profile.
Fig. 13. DMD rapid programmable tunable light source with three center wavelengths, i.e., 1531.50, 1542.00, and 1552.25 nm.
10 November 2006兾 Vol. 45, No. 32 兾 APPLIED OPTICS 8313
the micromirror coordinates. The technique proposed in this study is fully digitally programmable and pro-vides a simple and versatile means of synthesizing various light patterns. Hence it is suitable for applica-tion in optical communicaapplica-tion systems, sensing sys-tems, and fluorescence microscopy.
The authors gratefully acknowledge the finan-cial support provided to this study by the Na-tional Science Council, Taiwan, under grant NSC 93-2212-E-006-093. Also, funding from the Ad-vanced Optoelectronic Technology Center, National Cheng Kung University under projects from the Min-istry of Education and the National Science Council (NSC 95-219-M-009-008) of Taiwan is gratefully acknowledged.
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Microsc. 96, 317–331 (1999).
3. L. J. Hornbeck, “Digital light processing for high-brightness, high-resolution applications,” Texas Instruments, 12 Feb-ruary 1997, http://www.dlp.com/dlp_technology/images/dynamic/
white_papers/141_hornbeck.pdf
4. N. A. Riza and S. Sumriddetchkajorn, “Fault-tolerant dense multiwavelength add– drop filter with a two-dimensional digital micromirror device,” Appl. Opt. 37, 6355– 6361 (1998).
5. N. A. Riza and S. Sumriddetchkajorn, “Digital controlled fault-tolerant multiwavelength programmable fiber-optical attenu-ator using a two-dimensional digital micromirror device,” Opt.
Lett. 24, 282–284 (1999).
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Bryce, “Dynamic optical filter in DWDM systems using the DMD,” Solid-State Electron. 46, 1583–1585 (2002).
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相關著作
期刊論文
1.
Chuang, C. H. and *Lo, Y.L., “Digital Programmable Light Spectrum Synthesis
System Using the Digital Micro-mirror Device,” Applied Optics, Vol. 45, No. 32, pp. 8308-8314, November 2006. (IF: 1.637); 17/55 (Optics). (獲選為國際知名期 刊 Applied Optics 的 11 月份封面介紹, 對台灣學術能見度有一定地提昇)
研討會論文
1.
莊錦和、*羅裕龍, "DMD 晶片式光源頻譜合成系統,” 光學元件與系統設計
E1N-48418，2005 台灣光電科技研討會
2.
莊錦和、*羅裕龍, “DMD 晶片可程式化光源頻譜濾波系統,” 新興工程技術，
pp. 1177-1182，2005 中國機械工程師學會第二十二屆全國學術研討會
3.
Chuang, C.H. and *Lo, Y.L., “Using Digital Micromirror Device for Digital
Programmable Light Spectrum Synthesis System,” Accepted by Society of Experimental Mechanics Annual conference, 2006.
4.
莊 錦 和 、 * 羅 裕 龍 " Using the Digital Micromirror Device for Digital
Synthesizing Light Spectrum", E10-007 2006 中國機械工程師學會第二十三
屆全國學術研討會
計畫成果自評
本計畫執行所得之成果架構符合當初之實驗架構，但應用方面和當初設定之
FBG 訊號分析儀器更為擴展為光源頻譜合成系統，可針對任意對光源之頻譜進行 各種波形之合成，應用面相當廣泛如：光纖通訊、雷射頻譜合成、單光儀、頻譜 分析儀等。其技術之成果更為知名期刊 Applied Optics 獲選為當期之封面介紹 (詳見附錄)，可見本計畫所得之成果深受重視，相關之研究也持續進行。
本計畫之技術將下一步將應用於近場光學顯微技術，利用光源頻譜合成技術
得到不同之近場光學影像，加以分析即可得知量測樣品針對不同之頻譜所產生之
樣品特性，相當具有研究價值，因此，國科會所支持本計畫所得技術與衍生之研
究相當豐碩。
附錄