Wavelength-multiplexed digital holography for quantitative phase measurement using quantum dot film

Sungbin Jeon; Jae-Yong Lee; Janghyun Cho; Se-Hwan Jang; Young-Joo Kim; No-Cheol Park

doi:10.1364/OE.26.027305

1. Introduction

One of the major applications of digital holography (DH) is in quantitative phase imaging (QPI) [1–3]. Using either coherent or partially coherent light sources, the complex amplitude of the object wave from the hologram images could be rapidly obtained with numerical methods. Because the wavefront is modulated by the thickness or height of the object, the three-dimensional (3D) information of the object is reconstructed by calculating the optical path difference (OPD) between the object beam and reference beam. Because QPI with DH uses phase data and is based on a wide-field optical system, it could achieve axial resolution in the nanometer scale and square field-of-view (FOV) in the millimeter scale. Compared with other scanning-based 3D measurement methods, DH acquires several images with an image sensor such as a charged-couple device (CCD), resulting in much faster measurement speed. Therefore, many applications for biology [4,5], surface topography [2,6], and micro-optical components [7,8] have been studied for decades using DH method.

Despite all these advantages, practical QPI systems using DH have several constraints. Because DH is based on interferometric procedures to record the object wave, the captured holograms also include the speckle noise from the coherent light source, which degrades the quality of reconstructed data. Many post-processing algorithms could be applied to reduce the noise [9,10], but they require additional calculation time, slowing the process. Also, since QPI uses a phase profile wrapped within the bounds of [-π, π], an OPD longer than the wavelength could not be measured. While the FOV is reasonable, the axial range of the conventional system is still limited. Numerical methods for recovering unwrapped phase values have been proposed [11–13], but the accuracy or resolution is hugely depended on the noise level of holograms. Moreover, a highly inclined or stepped profile greater than the illuminating wavelength cannot be resolved numerically. Therefore, the QPI system with DH is utilized for objects of thin thickness or low height, with relatively smooth surfaces or generally less scattered internal structures [14].

To overcome these drawbacks, low-coherence [15] and dual-wavelength [16] DH have been studied. Low-coherence DH uses a light source with a wider wavelength bandwidth for lower temporal coherence, such as a light emitting diode (LED) [17–19], to capture holograms with less speckle noise. Because low-coherence light sources have relatively short interference ranges in the micrometer scale, they are sufficient for microscopic 3D measurement. Since an off-axis configuration could be applied for single-shot measurements [20,21], a phase-shifting DH could reconstruct the object wave with maximum frequency data, which is more suitable to QPI. To extend the axial range, the dual-wavelength unwrapping method was developed by combining two phase profiles which are reconstructed from sets of holograms acquired using light sources with different wavelengths [22–24]. To take advantage of both low-coherence and dual-wavelength methods, DH systems with a single low-coherence light source which is filtered or modulated to generate dual-wavelength interferograms have been proposed [25,26]. These studies showed relatively lower noise levels and the extend range of axial measurement in the simple and robust system. However, those dual-wavelength methods required two times more holograms for reconstruction, which increases the acquisition time. In the case that either the objects or systems are moving during image capture process, the dual-wavelength method produces extra errors, making it not applicable for the fast-moving case.

Recently, an in-line multi-wavelength phase-shifting DH reconstruction technique was proposed, which uses wavelength-multiplexed light sources [27]. Compared with the conventional dual-wavelength method which captures the phase-shifted holograms of each wavelength separately, this wavelength-multiplexed technique simultaneously records interferograms with two wavelengths and numerically reconstructs each complex amplitude. In this approach, a smaller number of holograms are needed to completely reconstruct the object wave and quantitative phase profile. Compared with previous methods, the wavelength-multiplexed technique could reduce and simplify the procedures to acquire holograms. However, to generate multi-wavelength illumination, multiple monochromatic light sources need to be combined, which increases the complexity and sensitivity of alignment of the system.

In this paper, we propose a practical dual-wavelength DH system for QPI with the wavelength-multiplexed technique. Quantum dot (QD) film can construct multiple wavelengths from a single light source. QD is a kind of nanophosphor that can convert a short wavelength light of high-energy to a long wavelength light of low-energy by controlling the particle sizes [28,29]. Thus, QDs show novel characteristics as a wavelength converter, including the generation of controllable emission wavelengths with narrow bandwidth using same materials of different particle sizes. While our previous research showed the possibility of QD film as an illumination source of dual-wavelength DH [26], it used separated two QD films where the change of QD film is required during the acquisition of holograms, resulting in the delayed measurement time and decreased resolution. Basically, QDs have an advantage to manipulate the resultant spectral distributions with respect to the size distribution of QD particles. To generate a wavelength-multiplexed light source in the proposed system, two different particle sizes of QDs are mixed and fabricated into a single film after controlling their optical characteristics to realize the maximum performance. By adapting the QD film, two low-coherence beams could be simultaneously illuminated into the interferometer from only a single LED without additional components. Because fewer wavelength-multiplexed holograms are required for dual-wavelength reconstruction compared to conventional methods, the proposed system takes both advantages of the simple system configuration with fast measurement as well as the low noise level with the enhanced axial range resolution. The experimental setup and reconstruction procedure of the proposed dual-wavelength DH system are described with the quantitative measurement and analysis on the sample of relatively high step.

2. Dual-wavelength digital holography with wavelength-multiplexed light source

2.1 Experimental setup

Figure 1(a) represents the configuration of the proposed system. To measure the surface height profile, a reflective phase-shifting DH setup using a Michelson interferometer is utilized. A 405-nm LED (Luminus, CBT-90) was used as a light source to excite the QD wavelength converter film that has dual-peak center wavelengths with full-width half-maximum (FWHM) of 30 nm each. Since the converted beam from the QD film emits isotopically, a short-pass filter (Semrock, FF01-468/SP-25) is attached between the LED and the QD film to reflect the back-illuminated converted beam to the object. A long-pass color filter (Semrock, LP02-488/RU-25) is also placed after the QD film to block the non-absorbed 405-nm light and avoid the illumination of unwanted wavelength light to the object. Because the converted beam is assumed spatially incoherent, a spatial filter and collimator are needed to manipulate the plane wavefront to create enough spatial coherence. After being divided by a 50:50 beam splitter, the object beam is reflected by the sample and recombined with the reference beam to generate an interferogram. In the reference arm, a flat mirror is attached on a piezo-electric transducer (PZT) actuator for modulating the phase of reference wave in the nanometer scale. The interferograms are recorded by a 2050 (H) × 2448 (W) CCD camera (Sony, XCL-5005) with a pixel pitch of 3.45 μm. A 4f imaging system is also included before the CCD image sensor to collect more light from the holograms focused on the sample plane, which is benefit to increase signal-noise ratio (SNR) of the reconstructed object information.

Fig. 1 Optical configuration of the proposed setup. LED, light emitting diode; PZT, piezo-electronic transducer; CCD, charge-coupled device; PC, personal computer.

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To generate the wavelength-multiplexed light source, a dual-peak QD film was fabricated. In this system, two different sizes of CdSe/ZnS phosphors of core/shell structures are selected with the center wavelength of 580 nm and 630 nm, respectively. First, each QD phosphor was dispersed separately in toluene solution. To fabricate the film, both solutions were then mixed on a UV curing polymer (Minuta technology, MINS-ERM) by controlling the relative concentration ratio. For the uniform mixing and dispersion of both QDs, the QD-polymer mixture was blended with a magnetic stirrer in the fume hood for 24 hours. During this process, the toluene solution was evaporated. Then, the QD-polymer mixture was dispensed on the glass substrate and pressed with the Polyethylene terephthalate (PET) cover film. A gap gauge was also used between the glass substrate and PET film to control the thickness of QD film. After exposing the QD-polymer mixture to sufficient UV light for five minutes, the QD film on the glass substrate was completed.

For the use in the wavelength-multiplexed DH system, the resultant light source needs to satisfy the following characteristics. First, it is required to separate two peaks emitted from the QD film clearly without less overlapping in the middle wavelength range. Second, the intensity of two peaks needs to be matched for the same signal-to-noise ratio (SNR) between the reconstructed phase profiles. The base data for the weight percent (wt%) and thickness for the fabricated QD film were determined from our previous research [26]. In the multi-wavelength QD mixture film, however, we have to select the mixture ratio of different size of QDs to realize same intensity of dual-peaks, since each QD has a little difference in the conversion efficiency and absorption spectrum. Moreover, the self-quenching effect and reabsorption phenomenon cause a noticeable difference in the converted intensity between the two peaks [30]. Therefore, the relative mixture ratio of two different QDs needs to be determined by experimentally before the fabrication of final QD film. Through the pre-tests, total weight percent of QDs and thickness of the fabricated film were fixed as 20 wt% QD and 50μm, respectively. A quantum yield measurement system with an integrating sphere (QD-1000, Otsuka) was used for measuring spectral distribution of the light converted from the QD film. As shown in Fig. 2, the intensity balance between two peaks is almost equally matched when the mixture ratio of 580 and 630 nm QDs was controlled with a ratio of 5:1. The resultant dual-peak wavelengths of the QD film were measured as 590 nm and 635 nm, respectively, since there is a wavelength shift up to 15nm for the light converted from the highly concentrated QD film due to the reabsorption issue, as shown in our previous report [26]. In addition, due to the reabsorption issue as well as the limited total volume of QDs in the film, the fabricated dual-peak or multi-color QD films has usually resulted in the decreasing tendency of emission efficiency and light intensity compared with the case of a single wavelength QD film [31]. This phenomenon can be improved by modifying the film fabrication procedure, including the use of patterned QD structure in the film [32]. Applying high-power LED as an excitation source may be a possible solution to increase the converted light intensity.

Fig. 2 Normalized spectral distributions of the fabricated dual-peak QD film with different mixture ratios. The inset means the relative mixture ratio of 580 and 630nm QDs in the QD film.

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2.2 Reconstruction of wavelength-multiplexed holograms

Unlike a conventional single-wavelength phase-shifting DH, a wavelength-multiplexed digital hologram requires the relatively complex procedure to measure its phase profiles: 1) separation of each object wave from multiple holograms by a numerical method, 2) dual-wavelength reconstruction for extending the axial height range over the half wavelength, and 3) post-processing of the measured data to reduce errors and enhance the accuracy. In our setup, the light source is assumed as the summation of two quasi-monochromatic beams with different center wavelengths, λ₁ and λ₂. Let $O_{k} (x, y) = | O_{k} (x, y) | e x p (i ϕ_{O_{k}})$ (the object wave with phase $ϕ_{O_{k}}$ ) and $R_{k} (x, y) = | R_{k} (x, y) | e x p (i ϕ_{R_{k}})$ (the reference wave with phase $ϕ_{R_{k}}$ ) for each wavelength λ_k, where k = 1,2. Moving the reference mirror, i.e. changing OPD, modulates the phase in different amount regards to the wavelength; therefore, the intensity I of multiplexed holograms could be expressed as:

\begin{array}{l} I (x, y; ϕ_{R_{1}}, ϕ_{R_{2}}) = I_{0} (x, y) + 2 | O_{1} (x, y) | | R_{1} (x, y) | \cos (ϕ_{O_{1}} - ϕ_{R_{1}}) \\ + 2 | O_{2} (x, y) | | R_{2} (x, y) | \cos (ϕ_{O_{2}} - ϕ_{R_{2}}), \end{array}

where I₀ is the sum of zero-order terms i.e. I₀(x,y) = |O_k(x,y)|² + |R_k(x,y)|². To calculate and separate each object wave, the wavelength-multiplexed method proposed by Tahara et al. could be used as follow [27]. The five holograms with different amounts of reference phase shift could be written as the matrix form:

(\begin{matrix} I (x, y; 0, 0) \\ I (x, y; α, β) \\ I (x, y; 2 α, 2 β) \\ I (x, y; 3 α, 3 β) \\ I (x, y; 4 α, 4 β) \end{matrix}) = (\begin{matrix} 1 & 1 & 0 & 1 & 0 \\ 1 & \cos α & \sin α & \cos β & \sin β \\ 1 & \cos 2 α & \sin 2 α & \cos 2 β & \sin 2 β \\ 1 & \cos 3 α & \sin 3 α & \cos 3 β & \sin 3 β \\ 1 & \cos 4 α & \sin 4 α & \cos 4 β & \sin 4 β \end{matrix}) \times (\begin{matrix} I_{0} (x, y) \\ 2 | R_{1} (x, y) | Re (O_{1} (x, y)) \\ 2 | R_{1} (x, y) | Im (O_{1} (x, y)) \\ 2 | R_{2} (x, y) | Re (O_{2} (x, y)) \\ 2 | R_{2} (x, y) | Im (O_{2} (x, y)) \end{matrix}),

where α and β are the amount of phase shift of each wavelength between image acquisitions. Since the left and the first right matrix terms in Eq. (2) are known, the far right matrix can be explicitly calculated. From the matrix, the object wave could be calculated by

\begin{array}{l} O_{1} = \frac{1}{2 | R_{1} (x, y) |} {(2 | R_{1} (x, y) | Re (O_{1} (x, y))) + i (2 | R_{1} (x, y) | Im (O_{1} (x, y)))}, \\ O_{2} = \frac{1}{2 | R_{2} (x, y) |} {(2 | R_{2} (x, y) | Re (O_{2} (x, y))) + i (2 | R_{2} (x, y) | Im (O_{2} (x, y)))} . \end{array}

In Eq. (3), the intensity of the reference wave |R_k| should be known to obtain correct object waves. In the QPI system, however, only phase data is required to measure the information of the object, and therefore, it could be calculated by simply dividing the elements:

\begin{array}{l} ϕ_{O 1} (x, y) = \tan^{- 1} {\frac{2 | R_{1} (x, y) | Re (O_{1} (x, y))}{2 | R_{1} (x, y) | Im (O_{1} (x, y))}}, \\ ϕ_{O 2} (x, y) = \tan^{- 1} {\frac{2 | R_{2} (x, y) | Re (O_{2} (x, y))}{2 | R_{2} (x, y) | Im (O_{2} (x, y))}} . \end{array}

The wavelength-multiplexed algorithm in the proposed system needs only 2N + 1 image acquisitions with different reference phase shifts to reconstruct phase profiles with N different wavelength channels, using only a single light source. In contrast, conventional multi-wavelength methods require 4N holograms and use a four-step phase-shifting algorithm for reconstructing robust quantitative phase profiles as well as additional procedure to change illuminations. Therefore, the wavelength-multiplexed technique could improve measurement speed over the conventional method.

3. Experimental results

To verify the effectiveness of the proposed system, a measurement was conducted for the sample of step height of 700nm which is considered as a difficult height profile to be meausred using a single-wavelength DH system of visible light with single set of holograms. The measurement results are presented in Fig. 3, which are acquired using the proposed dual-wavelength DH system, as shown in Fig. 1. Figure 3(a) shows one of 5 in-focus holograms of the sample with shifted reference phases. Using Eqs. (1)–(4), two sets of the phase data for the object wave from each wavelength are extracted independently. Because the wavefronts of the object wave are distorted by optical components included in the proposed system, wavelength-specific aberrations are also included in the simultaneous illumination of the two wavelengths. Therefore, the numerical processing for removing the aberration is required for the precision measurement [33,34]. In this paper, the linear regression method using the Zernike polynomial is used for estimating and eliminating the wavefront distortion of the phase profiles [35]. Figure 3(b) and 3(c) show the images from the beam of 590 nm and 635 nm wavelength after the compensating process for the aberration, respectively. Figure 3(e) also shows the cross-sectional phase profiles acquired simultaneously from two wavelengths where the wrapped phases with single-wavelength do not reflect the proper values of actual height.

Fig. 3 Results of the proposed technique: (a) one of the acquired wavelength-multiplexed holograms. Reconstructed and separated phase profiles of (b) 590 nm and (c) 635 nm wavelength emitted from both QDs. (d) Combined dual-wavelength phase profile from (b) and (c). (e) Cross-section profiles of 590 nm (top) and 635 nm (bottom) QDs. (f)-(i) Cross-section profiles of the region marked on (d), with line width (e) 1 mm, (f) 200 μm, (g) 100 μm, and (h) 50 μm respectively. (j) Detailed measurement result of the profile from the dashed area of Fig. 3(f), compared with the commercial probe profilometer.

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Then the dual-wavelength phase data is calculated from the differences between two profiles to obtain the extended axial information of the sample with a synthetic beat wavelength Λ. In a reflective system, this information could be converted to the surface height h of the sample as

h = \frac{ϕ_{O 1} - ϕ_{O 2}}{4 π} Λ,

where Λ is defined as Λ = λ₁ λ₂/| λ₁ - λ₂|. Figures 3(f)–(j) show the results of these calculated sample heights. To improve the accuracy of the measurement, several numerical methods are additionally adapted in this study, such as the reduction of the amplified noise during dual-wavelength reconstruction and the calculation of phase ambiguities using the method proposed by Gass et al. [22]. Also, a total variation (TV) algorithm is applied for denoising, especially to restrain the Gibbs phenomenon while conserving the sharpness of the image [36]. Although the effect of edge diffraction was relatively reduced due to the recorded image with the focused beam from the sample plane in this study, the edge diffraction noise was also considered [37,38].

Because the low-coherence, dual-wavelength DH system shows better accuracy than other commercial measurement devices [25,39], our measurement result is compared with that of a commercial probe profilometer (Brucker, DektakXT), as presented in Fig. 3(j). After a probe scanned the surface of the sample (see the red mark in Fig. 3(f)), almost identical position on the sample are selected to be measured by the proposed system. The mean heights from the profilometer and the proposed system were measured as 746.78 nm and 745.23 nm, respectively. The standard deviation for the profile calculated from the proposed system is 2.42 nm, compared to 2.24 nm for the commercial probe profilometer. Thus we can confirm that the proposed system can achieve an accurate measurement with the extended and low-noise axial range as well as the simpler and faster hologram acquisition procedure compared with the conventional methods.

4. Conclusions

In this paper, we proposed a new wavelength-multiplexed DH system for the QPI measurement of surface topography. A QD-based dual-peak wavelength converter was adapted to realize many advantages such as the compact system, the reduction of acquisition procedure to save measurement time, the decreased speckle noise, and the extended axial range of measurement. By determining the appropriate mixture ratio of two different sizes of QDs, the resultant spectral distribution resulted in identical peak intensity, which is required for utilizing the QD film as a single light source in the proposed system. From experimental measurement results for a step sample of 700nm, it was verified that the proposed system allows an extended axial range compared to the single wavelength system. The standard deviation of the surface topography measurement in the proposed system is less than 3nm, comparable to that of a commercial probe profilometer. Finally, the simple configuration of components and the reduced acquisitions of phase-shifted holograms in this wavelength-multiplexed DH system could also be advantages to be applied to many other fields.

Funding

National Research Foundation of Korea (NRF) (2016R1A2B4008869).

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Wavelength-multiplexed digital holography for quantitative phase measurement using quantum dot film

Abstract

1. Introduction

2. Dual-wavelength digital holography with wavelength-multiplexed light source

2.1 Experimental setup

2.2 Reconstruction of wavelength-multiplexed holograms

3. Experimental results

4. Conclusions

Funding

References

Cited By

Figures (3)

Equations (5)

Optics Express