2.1.

Speckle Noise

There are two types of optical coherence, spatial coherence and temporal coherence. Spatial coherence is the degree of order between light waves at different points in space. In contrast, the temporal coherence of light is the degree of order between lights emitted from the same point at different times. The temporal coherence is maximum when the emitted light contains a single wavelength, and it becomes lower as more light of different wavelengths is contained. In other words, the wider the wavelength band, the lower the coherence.

Figure 1 shows a schematic diagram of the principle when speckles are visually recognized. Speckle noise is random spotty visual noise observed when spatially and temporally coherent light such as LD light is scattered on a rough surface.¹⁶ The interference pattern formed on the retina deforms along with the wavefront of the light incident on the retina, so when the angle of incident light changes due to the change in pupil diameter, the visible speckle pattern also deforms.

Fig. 1

Schematic diagram of human eye recognizing speckle.

When quantitatively evaluating speckle, speckle contrast $C_s$ is used as an index to indicate speckle intensity, as represented by the following equation:

In this case, the speckle contrast ratio and the bandwidth ratio are inversely proportional. Therefore, if the bandwidth is adjusted steplessly, the speckle contrast can be freely controlled.

2.2.

Effect of Coherence on CGH Reconstructed Image

In holography, there is a close relationship between the resolution of the reconstructed image and the coherence of the light source.¹² In general, holograms cannot image a bright spot smaller than the emission size of the light source due to the diffraction limit. Therefore, reducing the emission size and increasing the spatial coherence are directly linked to improving the resolution of the reconstructed image. In addition, CGH is calculated for a specific wavelength, and it is assumed that the reconstruction light has the same wavelength.

Considering the case where the CGH calculated at a specific wavelength is reconstructed at a slightly different wavelength, an image is formed at a position that deviates from the target spatial coordinates accordingly. When a light source has wavelengths with a wide bandwidth, the convergence of points with different spatial image forming positions continuously causes a blurring effect, which reduces the sense of resolution. In other words, the more the temporal coherence increases, the more this blurring effect is eliminated, and as a result, the resolution of the reconstructed image is improved.

The sense of resolution of the reconstructed image is improved using spatially and temporally coherent light. However, as described in the previous section, light with high coherence forms strong speckles, so a higher coherence does not necessarily mean that the light source is more suitable for holographic reconstruction. Therefore, to ensure the quality of the reconstructed image, the light source should be well balanced such that it ensures a certain degree of coherence for the sense of resolution while reducing the visibility of speckles.

2.3.

Laser Phosphor Light Source

In general, LDs, which are spatially and temporally coherent light sources, are widely used for the reconstruction of electro-holography. However, because of the high coherence of LDs, speckle noise can significantly degrade image quality, so high-brightness LEDs are often used to reduce temporal coherence. However, the brightness of an LED per unit area is low, making it difficult to attain sufficient brightness if the size of the light emitting surface is reduced to ensure spatial coherence. Therefore, we focus on a projector light source that excites a yellow phosphor with a high-power blue LD that is temporally incoherent but has high intensity brightness in the same light-emitting area.

Figure 2 shows a schematic drawing of an optical system using a yellow phosphor as a light source in a projector. Many projectors equipped with solid-state light sources with high luminous flux have multiple high-output blue LDs as light sources, and more than half of the light is focused on one point on the yellow phosphor to excite yellow light.¹⁸ Here, the light converted into fluorescence by the yellow phosphor of the projector has a moderately wide FWHM of about 100 nm centered on the green band and is high-power light of about several watts to several tens of watts. Thus, it should be a suitable light source for adjusting temporal coherence.

Fig. 2

Schematic diagram of yellow phosphor excitation structure in projector.

The light from the yellow phosphor is collimated and incidents the linear polarizer as parallel light. The output light is a high-power parallel light with linearly polarization. These features are important for obtaining sufficient cut-on/off characteristics in the bandwidth adjuster, which will be described in Section 3.

3.1.

Incident Light Angle Characteristics of Dichroic Mirror

A dichroic mirror has a structure in which dielectrics with different refractive indices are formed into thin films by vapor deposition or similar processes, and films with high refractive indices and films with low refractive indices are alternately laminated. Due to this structure, the light reflected at each interface has a different phase difference, and the interference between them makes it possible to selectively reflect or transmit a specific wavelength. The light obliquely incident on each layer has a smaller phase difference than the light vertically incident. Therefore, when the angle of incident light to the dichroic mirror changes, the phase difference between the incident light and the reflected light changes accordingly, and the transmittance characteristic changes. Because the cut-on/off wavelength is generally shifted to the shorter wavelength side when the light with a larger incident angle on the dichroic mirror, this phenomenon is called blue shift.²² This is the incident light angle characteristic of the dichroic mirror.

The characteristics received when light is obliquely incident on the dichroic mirror can be obtained by calculating the convolution integral of the angular characteristics of the dichroic mirror and the normalized light distribution of incident light intensity. Figure 3 shows the wavelength characteristics of three types of light (40 deg, 45 deg, and 50 deg) with different incident angles, and it can be seen that the cut-on wavelength differs depending on the incident angles. When light with multiple incident angles is included, the solid line characteristic is obtained as the sum of their convolutions. Therefore, the parallelism of light is important for the slope-characters of the cut-on wavelength.

Fig. 3

Dependence of incident light angle on transmittance in a dichroic filter.

The parallel light whose incident light angles are only components that completely match the aforementioned angles receives the transmittance characteristics directly from the dichroic mirror. Therefore, the cut-on wavelength is the same at 525 nm for both the light distribution of the incident light with a wide angle (solid line) and that of parallel light (dashed line). However, the slope of the transmittance characteristic is steeper when the incident light is parallel light (dashed line) than in other cases. For this reason, the light incident on the dichroic mirror should ideally be close to parallel light.

In the case of oblique incidence, s-polarized light and p-polarized light can be defined by the difference in the vibration direction of the electric field with respect to the plane of incidence. The boundary conditions when light is transmitted or reflected at each boundary surface between air and multilayer films differ depending on this polarization state, so the transmittance/reflectance characteristics are shifted along the wavelength axis depending on the polarization state of the incident light. Therefore, if the light incident on the dichroic mirror contains both s- and p-polarized light, the slope characteristics become poor as described previously.

3.2.

Implementation of BPF with Variable Bandwidth

The bandwidth adjuster consists of LPF and SPF with an angle adjustment mechanism using a turntable as shown in Fig. 4. By cutting short wavelength light with LPF and cutting long wavelength light with SPF, the BPF allows the light in the band between their cut-off wavelength to pass through. When a dichroic mirror is used as a cut filter, the more the collimation of the incident light collapses and the less linear the polarized light, the poorer the slope characteristics become due to the above-mentioned angular dependence. Therefore, it is important that the light incident on the filter is parallel and has a single linear polarization. Based on these characteristics, by passing parallel light with uniform polarization through this unit, this unit functions as a BPF with a variable transmission bandwidth and sufficient cut characteristics due to the angular dependence of each dichroic mirror.

Fig. 4

Bandwidth controlling unit.

If the rotation directions of the LPF and SPF are the same, the incident light is refracted by the thickness of each dichroic mirror, so the optical axis is unintentionally shifted. To solve this problem, the dichroic mirrors are rotated in opposite directions to cancel out the effects of optical axis deviation before and after the transmission of each dichroic mirror, thereby minimizing the amount of optical axis deviation.

Further, the cut-off wavelength of each dichroic mirror at 45 deg incidence should ideally be longer in SPF than in LPF. This is because in the BPF that combines LPF and SPF, such as that in this study, the adjustment range of the transmission wavelength band can be increased by taking into account the dependence on incident light angle. If this relationship were to be reversed, almost no light would pass through the BPF with each mirror tilted at 45 deg, and the adjustment width by rotation would be wasted.

3.3.

Proposed System

Figure 5(a) shows the layout of the CGH reconstruction optical system to which the proposed light source device is applied, and the actual photograph is shown in Fig. 5(b). The proposed device is divided into a parallel light generation section, a bandwidth adjustment section, and a point light source generation section for each function. In the parallel light generation section, a commercially available 3LCD projector (EF-100W, EPSON) was modified as described in Sec. 2.3 and placed such that parallel light with high brightness could be obtained. The light source is a blue LD and yellow phosphor, and the maximum luminous flux is 2000 lm. This makes it possible to generate high-brightness parallel light that is linearly polarized. By making this light incident on the bandwidth adjustment section, a sufficient cut characteristic is obtained from the dichroic mirror. The LPF and SPF used in this device are the fluorescence dichroic filter ($\text{cut-on wavelength}=525\mathrm{nm}$, #67-081) and the dichroic SPF ($\text{cut-off wavelength}=550\mathrm{nm}$, #69-215) from Edmund Optics. The results of s-polarized transmittance characteristics measured using a spectrophotometer (UH4150, Hitachi) are shown in Fig. 6. When scanning spectrometers that utilize diffraction gratings or prisms, the measured slope characteristics of the filter change depending on the band width of the scanning light.¹⁹ The line in Fig. 6 is the result of measurement with the band width of 5 nm.

Fig. 5

(a) Proposed system layout and (b) actual appearance.

Fig. 6

s-polarized angle characteristics of each dichroic mirror.

After the aforementioned bandwidth adjustment unit is implemented, a point light source generation unit is arranged. An objective lens is placed in the point light source generation unit, and parallel light whose bandwidth has been adjusted is imaged at the back focal position. By arranging an aperture at this focal position, the present light source device functions as a light source in which the opening of the aperture acts as a light emitting surface. The projector used here has a nominal brightness of 2000 lm, but in this device, we used an output equivalent to 1000 lm in consideration of the thermal effects of the optical parts near the condensing part, such as the objective lens and aperture.

After the developing proposed light source device, we arranged a general phase-type electro-holography reconstructing optical system. A $4f$ optical system is arranged in this reconstruction optical system, and it is possible to remove the light that hinders viewing the reconstructed image, such as the zeroth order light.²³ The light emitted from the aperture of the proposed light source device is collimated by the subsequent collimating lens and enters the LCD on which the hologram is displayed. The light diffracted by the LCD enters the $4f$ optical system together with the direct light. The direct light is condensed at the focal position of the front lens of the $4f$ optical system and blocked by the mask placed here. After that, the light is collimated again by the rear lens of the $4f$ optical system, and only the light necessary for reconstructing the holographic image reaches the observer. Such a path allows the observer to observe the bandwidth adjusted reconstructed image.

4.1.

Performance Test

The features of the proposed device are that the bandwidth can be adjusted freely and that it has high brightness because it is equipped with a high-power light source. To verify these two characteristics, we measured the spectrum on the liquid crystal panel surface and the illuminance immediately after the mask when the bandwidth was changed.

The parameters of the light source device in this experiment are shown in Table 1. For measuring illuminance and spectrum, T10A(KONICAMINOLTA) and CS2000A(KONICAMINOLTA) were used as instruments, respectively, and a standard white plate was placed on the measurement surface during spectrum measurement. The measurement positions of the spectrum and illuminance are shown in Fig. 7. The target of the center wavelength (CWL) of the transmission light was adjusted to 555 nm, which is the peak of the luminous efficiency function.

Table 1

Parameters of proposed system.

Fig. 7

Placement of the measuring instrument.

Figure 8 shows the measurement results of the transmitted light spectrum when the transmission bandwidth of the BPF is changed. Here, while the FWHM changes from 60 to 6 nm, the incident light angle to the LPF and SPF gradually decrease and increase, respectively.

Fig. 8

Evaluation result of spectra when adjusting bandwidth.

In the BPF with this configuration, the output light intensity greatly decreased when the FWHM fell below 6 nm, so the lower limit of the FWHM adjustment range in this system was 6 nm. Conversely, even if the incident angle to the SPF is 0 deg, the cut-off wavelength cannot be shifted further to the long wavelength side, so the upper limit of the FWHM adjustment range in this system was 60 nm. The CWL of transmitted light is 555 nm, verifying that the transmission band of the BPF can be adjusted as intended within the range from 6 to 60 nm.

The results of illuminance measurement are shown in Fig. 9, along with a green LD (532 nm) and a commercially available high-brightness green LED for reference. The illuminances of the LD and high-brightness LED shown in Fig. 9 were not actually measured but are examples of a commercially available light source. To facilitate comparison with the proposed system, the illuminances shown in the graphs are all converted values when the emission area, solid angle, and polarization state are adjusted to the measurement conditions of this study. The results in Fig. 9 demonstrate that the brightness decreases as the temporal coherence increases. This is because the integrated value of the spectrum is the emitted light energy, which can be considered an indication that the bandwidth adjustment mechanism functions correctly. Although the illuminance per $0.01{\mathrm{mm}}^2$ is not as bright as that of LDs, the illuminance when FWHM is adjusted to 6 nm, which is the narrowest band, is almost equivalent to that of high-brightness LEDs. We also determined that the illuminance with a FWHM of 30 nm or more can be used as a light source that is 1 order of magnitude brighter than a high-brightness LED.

Fig. 9

Brightness of proposed system.

4.2.

CGH Reconstruction Evaluation

Next, we reconstructed the CGH with the light whose bandwidth was adjusted using the proposed device and took pictures with the camera. The results demonstrated the relationship between the FWHM and the speckle contrast value. Images captured by camera are often used to calculate the speckle contrast. As described in Sec. 2.1, the speckle pattern depends on the light capture angle, so the camera’s $F$-number should be adjusted to the corresponding value of the pupil diameter so the imaging optical system has an modulation transfer function (MTF) equivalent to that of the human eye.²⁴ Here, the pupil diameter is a parameter that changes depending on the brightness of the surrounding environment and the reconstructed image.²⁵ Therefore, if the speckle visible to the human eye is to be faithfully constructed, the $F$-number of the camera should be changed for each brightness of the environment and the reconstructed image. However, as the purpose of this study was only to determine the effect of the coherence of the light source, the $F$ value was fixed at 7.1. This $F$-number is equivalent to a pupil diameter of 3.2 mm²⁶ when viewing images with the brightness of a typical indoor theater.²⁴ Using the captured image of the reconstructed image and the relational expressions of Eqs. (1)–(3), it is possible to quantitatively evaluate the relationship between the speckle intensity and the light source bandwidth from the captured image of the CGH reconstructed image.

The parameters of the proposed system and CGH parameters in this experiment are shown in Table 2. In the experiment, CGHs were calculated by the point-based method.²⁷ In this method, the surface of the object is treated as a collection of minute point light sources, and the interference fringes formed on the hologram surface by each object light source and the reference light are calculated and recorded as a hologram. Figure 10 shows a photograph of the reconstructed images. Figure 10(a) is an input object before CGH calculation, and Figs. 10(b)–10(h) are photographs of reconstructed images when the FWHM of the light is changed from 6 to 60 nm. Speckle noise occurs in these reconstructed images, and due to the difference in temporal coherence, it can be seen that the resolution of Fig. 10(h) is lower than that of Fig. 10(b), but the speckle noise is reduced. Figure 11(a) shows a graph in which $C_s$ is calculated by Eq. (1) using part of these images, and the relationship with each FWHM is plotted. The dashed line in Fig. 11(a) shows the theoretical curve estimated by Eq. (3) for FWHM of 30 nm. The calculation range of $C_s$ was set to the 512 pixel square area within the frame shown in Fig. 11(b). Although the results deviate from the theoretical curve, $C_s$ monotonically decreases with increasing FWHM. The cause of this deviation is discussed in Sec. 5.1. Thus, we determined that speckle noise can be controlled by adjusting the bandwidth of the light source and controlling the temporal coherence.

Table 2

Parameters of CGH reconstruction evaluation.

Fig. 10

Photograph of the reconstructed images: (a) input object data, (b) $\mathrm{FWHM}=6\mathrm{nm}$, (c) $\mathrm{FWHM}=10\mathrm{nm}$, (d) $\mathrm{FWHM}=20\mathrm{nm}$, (e) $\mathrm{FWHM}=30\mathrm{nm}$, (f) $\mathrm{FWHM}=40\mathrm{nm}$, (g) $\mathrm{FWHM}=50\mathrm{nm}$, and (h) $\mathrm{FWHM}=60\mathrm{nm}$.

Fig. 11

Speckle contrast calculated result: (a) FWHM versus speckle contrast and (b) calculation area of the speckle contrast.

5.1.

Speckle Contrast

The relationship between speckle contrast and bandwidth shown in Fig. 11 deviates from that shown in Eq. (3). Specifically, according to Eq. (3), the FWHM and the speckle contrast should have an inversely proportional relationship. However, when FWHM is narrow, the calculated $C_s$ values deviate from the theoretical curve shown by the dashed line in Fig. 11. There are two possible reasons for this. The first is that the spatial coherence is low because the size of the aperture used in this experiment is 0.1 mm × 0.1 mm. A device having a structure in which the spatial coherence can be freely adjusted would be needed to investigate further. The second reason is that the spectral shapes are different when the spectra normalized for FWHM and peak intensity are overlaid and compared for each FWHM as shown in Fig. 12. Previous studies^11,14,28 that investigated the relationship between FWHM and speckle noise often assume that the spectral shape of the light source is a Gaussian spectrum. Therefore, the FWHM used as an index of bandwidth in the proposed device may not necessarily be directly proportional to the temporal coherence. These two reasons are important factors to be considered in examining the relationship between controlled coherence and $C_s$ and should be investigated further.

Fig. 12

Normalized spectra of light source. Vertical and horizontal axes are normalized by intensity and FWHM, respectively.

5.2.

Brightness

The brightness measurement results of our study are shown in Fig. 8. The performance of the proposed system varies greatly depending on the light source used, i.e., the brightness of the projector. The EF100W used for the light source is a projector with a nominal brightness of 2000 lm, but considering the thermal safety of the optical parts, it was used at an output of about 1000 lm, so the maximum performance value in this system can be expected to be doubled. For example, if a projector whose brightness is 10,000 lm is installed in the same way, the brightness of the system can be expected to be about 10 times that of the results measured in this study. As a result, the difference in brightness widens further, and a light source about two orders of magnitude brighter than high-brightness LEDs should be feasible. A drastic improvement in brightness should be possible with the introduction of a high-output projector after ensuring the heat resistance of the optical components.