Structured illumination is widely used in the fields of optical metrology [1], such as 3D measurement [2–4], facial imaging [2,5], dental imaging [2], and super-resolution microscopy [6]. In the case of 3D measurement, the illumination patterns are roughly classified into dot and fringe patterns. The spatial resolution of the dot pattern depends on the size of the dot, while that of the fringe pattern is several hundredths of the fringe period since phase-shift methods can be applied [1–3]. Therefore, the fringe pattern is useful for highly accurate 3D measurements when a projector [1,2] or LED array [7] is utilized for illumination. With an on-chip size projector, it will be possible to realize an extremely compact 3D measurement system that positively impacts the mobile 3D measurement system as well as measurement in very narrow spaces, such as in-vivo environments.

In this context, the photonic crystal surface-emitting laser (PCSEL) proposed in Refs. [8–15], which utilized a 2D PC as a lasing cavity, is a great framework because of its compactness, high mode stability, and high directional beam control. On the basis of the PCSEL technologies, we incorporated the concept of holographic modulation into the 2D PC cavity. The holographic modulation is realized by a positional and areal shift of the holes in which the basic idea comes from the detour phase hologram [16–18] known since the 1960s. We introduced holographic modulation into the 2D PC and proposed an on-chip pattern projector, which we named the integrable phase-modulating surface-emitting laser (iPMSEL) [19–25]. So far, we have demonstrated a variety of patterns, including the structured illuminations such as large-scale dot patterns and fringe patterns [23]. However, unlike the dot pattern, the fringe pattern tends to cause speckle-like noise, which is an issue that needs to be addressed since this noise causes severe positional errors in the 3D measurement.

A clue to how to suppress the noise is the interference between neighboring dots in the far-field plane that degrades the quality of the beam pattern, i.e., a set of dot patterns. Figure 1(a) shows the far-field pattern (FFP) of vertical lines of dot patterns from the iPMSELs fabricated as in Ref. [23], which consists of continuous dots, while Fig. 1(b) shows lines of a dot pattern where all points along the vertical axis are thinned out. In the case of the continuous-dot lines, the dots become broader and grain-like noise and discontinuity are observed, while in that of the thinned-out lines, the dots are narrow as designed. Presumably, the continuous-dot lines show the presence of the interference between neighboring dots, which broadens the point spread function. Such interference between neighboring dots in the far-field plane presumably contributes to the noise in the fringe pattern. One approach to address this issue is thinning out the continuing points. This suppresses the broadening of the point spread function, as shown in Fig. 1(b), but it causes a discontinuity at the position where the dot is thinned out. It would be preferable to have an alternative approach that suppresses the interference between neighboring dots while providing a continuous pattern. In this Letter, we present a simple approach to reducing the noise of the fringe pattern on the basis of the idea that a 1D line of dot patterns with spacings between each dot is extended by a 1D focusing hologram.

 

Fig. 1. FFP of the line dot hologram patterns from the iPMSEL where (a) dots are continuous, and (b) every dot is thinned out. Yellow dot patterns schematically indicate alignment of the dot pattern in the far-field plane.

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The device structure is similar to that in the previous work [23] except for the holographic design. Before the explanation of the holographic design, the fabrication process is briefly described here.

Figure 2(a) shows the schematic of the device structure. First, the n-AlGaAs cladding layer, the i-InGaAs/AlGaAs active layer, and the i-GaAs layer are grown on the n-GaAs substrate by metalorganic chemical vapor deposition (MOCVD). Then the holographically modulated PC structure, where the hole is rotated on the periodic lattice point of the 2D PC in accordance with the phase distribution [as shown in Fig. 2(b)], is formed on the GaAs layer. In this case, the lattice constant (a), filling factor (areal ratio of the holes against the unit cell), and radius of the circle where the center of gravity of the hole is rotating (r), are 202 nm, 28%, and 0.08a, respectively. This layer simultaneously acts as a lasing cavity as well as a holographic modulator, so hereafter we call it the phase-modulating layer. After the formation of the phase-modulating layer, the p-AlGaAs cladding layer, and p-GaAs contacting layer are grown successively by MOCVD. Then the p and the n electrodes are formed by using an ordinary lithography process. The output beam is emitted by opening a window of the n-electrode where an anti-reflection coating is formed. As shown in Fig. 2(a), the output beam is one-dimensionally focused 1D dot patterns where the focal length is 0.1 mm and they then spread along an axis to form the fringe patterns.

 

Fig. 2. Device structure of the iPMSEL. (a) Perspective view, and (b) manner of hole movement in the phase-modulating layer.

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The holographic design of the 1D focusing beam is as follows. In the Fresnel diffraction integral [26], the diffraction field is expressed as a Fourier transform of the product of the complex object field and a quadratic exponential as

 

Fig. 3. (a) Schematic of the 1D focusing and (b) procedure of holographic design of the 1D focusing.

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Fig. 4. Phase distribution of the 1D focusing.

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Fig. 5. Fourier spectrum of (a) line of dots pattern and (b) 1D focusing including the ±1^st order beam.

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The iPMSEL is operated by the laser diode (LD) driver (ILX lightwave, LDP-3830) with the Peltier controller (Daitron, DPC-100). The FFP is acquired by the CCD camera (Hamamatsu, ORCA-05 G) through the FFP optics for narrow angle (Hamamatsu, A3267-15) and wide angle (Hamamatsu, A3267-12). The beam profile is measured by the beam profiler (Hamamatsu, Lepas-12). The FFP is shown in Fig. 6 in which pulse width, pulse duty, operation current, and temperature are 50 ns, 1%, 4 A, and 25°C, respectively. The FFP of a narrow angular range around surface normal is shown in Fig. 6(a). It shows the fringe patterns that aligned around 5° near the center. Compared with Fig. 1(a), grain-like noise and discontinuity due to the interference of the neighboring point are successfully suppressed in the 1D focusing fringe. Note that the slight broadening of the width shown in Fig. 6(a) might be caused by the broadening of the point spread function as shown in the PCSEL under high operation current [9]. It also indicates that the width of the fringe can be increased by increasing the operating current to some extent which is useful for adjusting the fringe pattern. Figure 6(b) shows the FFP in a wide angular range. The fringe extends over ±45°. Note that the fringe is distorted outside around ±30° because it extends linearly in the wavenumber space. The tendency of periodic mesh among flat screen, angular space, and wavenumber space is summarized in previous work [23]. Note that the phase-shifting method can be used to evaluate the 3D shape even in the distorted fringe. The slight interference seen in the upper and lower sides in Fig. 6(b) corresponds to that in the Fourier spectrum shown in Fig. 5(b).

 

Fig. 6. FFP of the 1D focusing iPMSEL in (a) a narrow angular range and (b) a wide angular range.

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To quantify the improvement, the fringe patterns between conventional continuous-dot lines, as shown in Fig. 1(a), and the 1D focusing pattern, as shown in Fig. 6(a), are compared as follows. First, the pixel error of the CCD camera is removed by processing the 3 × 3 median filter twice in ImageJ, since the pixel errors severely disturb the evaluation of the fringe. Figure 7(a) shows the 100 × 100 pixels from the center of Fig. 1(a) after removing the pixel error, while Fig. 7(b) shows that of Fig. 6(a). After removing the pixel error, mean value and standard deviation of the 10 × 1024 pixel in the central fringe as a reference for a line of fringe are calculated by using ImageJ. The fluctuation of the fringe is calculated by division of the standard deviation by the mean value. The fluctuation of the fringe in Fig. 1(a) is 30.5% while that in Fig. 6(a) is 7.6%, so the 1D focusing method improves the flatness by around four times. Thanks to avoiding the interference between neighboring dot patterns in the far-field plane, low-noise fringe patterns are achieved. We also evaluated the phase of the 1D focusing fringe patterns by using the 4-step phase-shifting method [2] in Supplement 1 which reflects the surface shape without severe speckle error.

 

Fig. 7. 100 × 100 pixels from the center of the FFP in (a) Fig. 1(a) and (b) Fig. 6(a) after removing the pixel error.

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In this Letter, we propose a simple method to obtain a low-noise fringe pattern on the basis of the idea that 1D line dot patterns having spacings between each dot are extended by a 1D focusing hologram. In contrast to the conventional continuous-dot array pattern, the grain-like noise and discontinuity in the FFP due to the interference between neighboring point patterns is avoided in our method. Although the 1D focusing fringe causes a slight distortion in the angular range above ±30°, this technique opens the way to highly accurate 3D shape measurement with chip-sized compactness.