Digital holography (DH) has been widely used in various research fields for topographic measurements of three-dimensional (3D) objects [1,2]. However, using DH systems in practice has several technical limitations. First, a coherent light source such as a laser, is generally used in digital holography for precise image measurements; however, it critically degrades images by introducing speckle noise [3]. Speckles are induced by high-coherence characteristics of light sources as signal noise during object measurements; thus, laser-based DH images include speckle noise. In addition, although DH could measure surface profiles with nanometer-scale axial resolution using the phase quantitative method, the height over the wavelength is wrapped from $-\pi$ to $+\pi$. In general, phase unwrapping can be performed [4] but, in the case of stepped or highly inclined height difference, the error persists. To resolve these limitations, dual-wavelength [5,6] and low-coherence methods [7–10] have recently been introduced to DH. Dual-wavelength DH captures multiple holograms with different wavelengths, and it calculates the phase by combining all reconstructed data. Compared with the conventional single wavelength method, the axial measurement range of the dual-wavelength method could be extended. Adapting a partial coherence light source such as a light-emitting diode (LED) is also advantageous for reducing speckle noise. While these methods still suffer from imprecise alignment, which affects the quality and accuracy of phase data, Jeon et al. [11] have proposed a compact and robust configuration by combining both techniques using a single LED with bandpass filtering. However, most of the initial beam power is blocked by filtering; thus, this approach necessitates a high-power light source. Because a typical LED has a Gaussian spectral distribution, the energy loss becomes severe if the filtered peak wavelength is far from the original one. Moreover, depending on the selection of filtered wavelengths, the intensities of any two filtered beams can be noticeably different, which can affect the signal-to-noise ratio (SNR) of the reconstructed data when using the dual-wavelength method [12].

Quantum dots (QDs) are nanophosphors that can be used to convert high-energy short wavelengths to low-energy long wavelengths by controlling the size of QD particles [13–15]. In previous works, QDs were used to replace wavelength converters such as phosphors or color filters in display applications, owing to their advantages over conventional LEDs [16,17]. QDs were also used as fluorophore and labeling materials to measure organic molecules in imaging applications, owing to their long-term stability and simultaneous detection ability [18,19]. QDs exhibit size-controllable emission-wavelength tunability and a narrow emission linewidth with an exact color index. In addition, QDs can be fabricated into films, which can easily be applied to practical imaging systems. From these characteristics, using QDs after a light source yields low-coherence wavelength converters with reasonable beam quality thus, QDs can be used as light sources for dual- or multi-color imaging applications, including DH. In this Letter, we propose an improved dual-wavelength low-coherence DH system with wavelength modulation, using a QD film-based wavelength converter. Because the peak wavelength of the QD-based light source is determined only by the distribution of particle sizes, the optical intensity of every wavelength is more uniform than that of LED bandpass filtering. The fabricated QD films were combined with a shortpass filter and color filter to improve the image quality of the DH system.

Figure 1 schematically shows the proposed QD-based dual-wavelength DH system. The configuration is based on a lens-less Michelson interferometer. As a light source, CdSe/ZnS QD films of core/shell structures, with full width at half-maximum (FWHM) of 30 nm, were illuminated by a 460 nm wavelength LED (Luminus, CBT-90). To distinguish two beams in terms of their spectral distributions during the dual-wavelength DH acquisition and reconstruction, two QDs with peak wavelengths of 590 and 620 nm were selected, where the wavelengths correspond to the FWHM of QDs in the solution. In addition, while these QDs could convert the input beam energy into desired wavelengths at specific quantum efficiency, the fabrication process of the QD film must be controlled carefully. Therefore, to obtain the sufficient characteristics of the light sources, we pre-tested the efficiency and peak wavelength of QDs, under various fabrication conditions. Table 1 lists the quantum efficiencies of the QD films prepared with 620 nm wavelength QDs. Although the high concentration and thickness of the film would have a merit to convert more input beams, the aggregation and re-absorption characteristics of QDs degrade the conversion efficiency of the resultant the QD film [20]. To simplify the tests, QD films were carefully selected as 10, 20 weight percent (wt. %) of concentration and 20, 50, and 100 μm of thickness. The concentration was controlled by adjusting a mixed quantity of QDs, while the thickness was controlled using gap gauges with target thicknesses of the films. Among the test conditions, the QD film with the concentration of 20 wt. % and thickness of 50 μm was selected owing to its highest quantum efficiency, i.e., maximal optical power after wavelength conversion. The spectral distribution for this film is compared with that for a filtered LED in Table 2 and Fig. 2. Here, the peak wavelengths of 602 and 635 nm QD films are prepared with the 590 and 620 nm wavelength QDs, respectively, since there is a peak wavelength shift after being formed as a film structure. As reported previously [20], the peak wavelengths of the initial QDs are shifted up to 15 nm after the fabrication of QD films. A quantum yield measurement system, including an integrating sphere (QE-1000, Otsuka), was used for comparing the relative intensities of the QD converted beam with those of the LED-based DH. Thus, it was found that the separation of the converted peak wavelengths between two QD films is larger than the FWHM of each beam, which is enough to be used in duel-wavelength DH. In addition, the measured converted intensity was $\sim 40\%$ of that of the initial light source. After comparing the normalized spectral distribution of LED-filtered light sources obtained using a red LED (Thorlab, M625L3) filtered by bandpass filters (Thorlab, FB620-10 and FB640-10, respectively), we could conclude that QD films can be advantageous for illuminating DH systems with more optical power, as shown in Fig. 2.

Table 1. Quantum Efficiencies of QD Films Prepared with 620 nm Wavelength QDs for Various Fabrication Parameters

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Table 2. Optical Characteristics of QD-Based Light Sources

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Fig. 1. Proposed digital holography system with the QD-based light source. LED, light-emitting diode; QD film, quantum dot film; PZT, piezoelectric transducer; OBJ, object; CCD, charge-coupled device; PC, personal computer.

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Fig. 2. Normalized spectral distributions of fabricated QD films, compared with those of filtered/nonfiltered red LEDs.

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In practice, however, because QDs emit highly distributed light, the actual beam power that reaches the interferometer would be lower than the initial one, as a result of collimation and spatial filtering. This optical power issue also occurs in LED-based low-coherence DH systems but, in the case of QD films, the light is emitted backward as well as forward, in an isotropic manner; therefore, half of the converted energy may be lost. To compensate for this energy loss, additional optical components should be introduced. Thus, a shortpass filter (Semrock, FF01-492/SP-25) is placed before the QD film to use the reverse illuminated LED light efficiently. Using this technique, the backward-propagating beam is reflected into a desired direction by the shortpass filter. A general red color filter used in display is also placed after the QD film to filter the blue lights which pass through the QD film without absorption.

In addition, similar to general low-coherence DH systems, a collimator and a spatial filter before the imaging part are required for increasing the beam spatial coherence. After collimation, the angular distribution of intensity becomes more concentrated in the imaging part. Further, because the light source is assumed to be spatially incoherent [21], the increase in the speckle noise by spatial filtering is negligible.

To capture the hologram, a four-step phase-shifting method is used for better image quality among the off-axis or in-line methods [22]. Holograms of each wavelength are captured with the same DH measurement system after changing the QD films of 620 and 635 nm as a light source, respectively. A flat mirror is attached to a piezoelectric transducer (PZT) to generate a phase-shifted reference beam by modulating the position of the mirror on the nanometer scale. Because the coherence length of the light source is on the order of tens of micrometers, the optical path length (OPL) between the reference and object arms should be matched. The interfered images are recorded digitally using a charge-coupled device (CCD) camera with the resolution of $2448(\mathrm{H})\times 2050(\mathrm{V})\text{pixels}$, with individual pixel dimensions of $3.45\mathrm{\mu m}\times 3.45\mathrm{\mu m}$ (Sony XCL-C500). From the four holograms of each wavelength, the phase data are calculated as

Figure 3 shows the results of the holographic reconstruction of each wavelength. As an object, a standard height sample (VSLI, SHS-1.8QC) was used [11]. Although the reconstructed data obtained using low-coherence QD light sources are more precise than those obtained using high-coherence DH, the quantitative phase profiles in Fig. 3 reveal two major errors that affect the reliability of topographic measurements. First, because the height difference exceeds the axial range of both wavelengths, the measured phase data only reflect the wrapped value within that wavelength, resulting in a different value and contrast, respectively. As discussed above, dual-wavelength reconstruction can resolve this limitation. From the spectral data in Table 2, the beat wavelength is calculated as 11.41 μm, which is $\sim 20$ times longer than that for the single-wavelength case. Since the optical path difference is doubled owing to the reflective interferometer configuration, a maximal height step of $\mathrm{\Lambda }/2$ can be measured using dual-wavelength DH. Second, systematic errors of both the light source and interferometer, which are defined as aberrations, appear in the phase data [23]. Although the aberrations for each wavelength are mostly identical and can be removed by phase subtraction, as in Eq. (2), wavelength-dependent errors remain. Therefore, before dual-wavelength calculations, both the calculation of and compensation for aberrations are required. For stability, in this Letter, we numerically approximated the aberration by the Zernike polynomial from the obtained phase profile [24].

 

Fig. 3. Results of DH reconstruction using a single QD-based wavelength converter designated for (a) 602 and (b) 635 nm.

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Figure 4 shows the dual-wavelength reconstruction results for the proposed system. To additionally enhance the profile’s quality, the phase ambiguity calculation method to avoid the noise amplification during the dual-wavelength process was applied by averaging the single-wavelength height profile $h_k$ [5,6]:

 

Fig. 4. Results of dual-wavelength DH reconstruction using the data in Fig. 3: error-corrected phase profiles of (a) 602 and (b) 635 nm QD light sources. (c) Two-dimensional and (d) 3D presentations of dual-wavelength height distribution. (e, f) Cross-sectional profiles of the red lines in (c). (g) Detailed profile from a dashed rectangle in (e).

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The result implies that QD-based light sources could be utilized in a DH system with a lower noise level, due to the higher optical power and wider bandwidth, compared with the LED filtering method. In addition, while conventional monochromatic LED has a limited bandwidth and nonuniform spectral distribution, a QD-based wavelength converter could adjust both peak wavelength and FWHM of each beam. Since the temporal coherence length of an optical system is related to the FWHM of the corresponding light source [25], wider bandwidths yield shorter coherent lengths i.e., a better SNR of the reconstructed image, while reducing the peak wavelength differences, enables the measurement of an extended axial range by a dual-wavelength method. By adapting QD materials with a narrow spectral range [26], more versatile systems are expected for the measurement of either higher steps or better quality.

In summary, we proposed a QD-based dual-wavelength DH system with a single light source. By using QD films with appropriate QD characteristics and film properties, the converted beam has been shown to exhibit higher and more uniform optical power than that generated using a bandpass-filtered LED system which, in turn, implies a higher SNR. By adapting the QD wavelength converter to the four-step phase-shifting DH, experimental results showed that a highly stepped sample over the wavelength could be measured with lower speckle noise. Thus, it was confirmed experimentally that a newly proposed imaging device in this Letter can yield higher-quality images than the previous DH system.