2.1.

Dark-Field Microscopy

To achieve a high contrast image of the specimen, a dark-field approach has been utilized. Generally, in dark-field microscopy, the specimen is illuminated with a hollow cone of light and therefore, the zero diffraction order, which falls out of the view of the imaging objective, is absent in the image, leading to a dark background. Hence, the highly diffracted orders, being scattered from the fine structures of the specimen, make the main contribution in the image formation (Fig. 1). Collecting only the high diffraction orders, the system delivers a higher resolution. On the other hand, due to the absence of the bright background, the small structures are visible with an enhanced contrast.

Fig. 1

Schematic of a dark-field microscope.

2.2.

Speckle-Field Illumination

In spite of transferring high spatial frequency, the scattered light creates a strong speckle noise in the case of using a coherent source for illumination. The created speckle pattern reduces the image quality and the high frequency information will be lost in the image. Therefore, implementing the dark-field approach in a coherent microscopic system seems to be challenging. We took advantage of the speckle noise itself to improve the image contrast. In this method, instead of using a uniform spot for illumination, the specimen is illuminated with a speckle-field (the experimental setup is illustrated in detail in the following subsection). Figure 2 represents the images of a given sea urchin larva recorded with different illumination conditions. A bright-field image of the larva is shown in Fig. 2(a), illuminated by a short coherence source (55 μm) with a wavelength of 405 nm. Figure 2(b) was obtained by illuminating the larva with the same light source as Fig. 2(a), but with 200 different speckle-fields and by averaging over the fields. Although a short coherence source has been utilized, Fig. 2(a) still suffers from the presence of coherence noise, which can be improved using a speckle-field illumination approach [Fig. 2(b)]. Figure 2(c) represents a dark-field image of the same larva illuminated by a 660 nm laser diode with a coherence length of $>1\mathrm{m}$. Due to the long coherence length, the speckle noise is dominant in the image, which is apparent in the enlarged section of Fig. 2(c). For the image shown in Fig. 2(d), the larva was illuminated in the dark-field mode with 200 speckle-fields and the final image has been derived by averaging over the fields. In the enlarged section of Figs. 2(c) and 2(d), one can clearly realize the contrast enhancement after illuminating with and averaging over various speckle-fields.

Fig. 2

(a) Bright-field image of a sea urchin larva illuminated by a short coherence source (405 nm). (b) The bright-field image obtained by illuminating the larva with 200 different speckle-fields and averaging over the fields. (c) The dark-field image of the same larva illuminated by a 660 nm laser diode. (d) The dark-field image taken after averaging over 200 speckle-field illuminations. The images are taken by a bright/dark-field objective ($20\times$, $\mathrm{NA}=0.45$).

2.3.

Dark-Field Digital Holographic Setup

Figure 3 represents a schematic of the dark-field digital holographic microscope. For dark-field illumination, a Nikon bright/dark-field objective with the magnification of $20\times$ and the numerical aperture of 0.45 has been utilized. The objective has the ability to operate both in dark-field and bright-field modes. An off-axis holographic setup has been arranged for the experiment. The blue colored (in the online version) beam path shows the capability of bright-field holographic microscopy. For simplicity, the reference beam path is only shown for the dark-field mode in the scheme. The illumination beam is redirected toward the dark-field objective using a ring-shaped mirror. The portion of the beam which passes through the center of the ring mirror is used as the reference beam. A pinhole is placed in the reference path to create a uniform reference wavefront. A laser diode with the wavelength of 660 nm has been selected for the dark-field illumination, as the biological tissue has a relatively higher scattering rate in this region of the visible spectrum. A short coherence (55 μm) laser diode operating at 405 nm was used for the bright-field mode. A SVCam-ECO charged coupled devices camera (SVS-VISTEK GmbH, Seefeld, Germany) with the pixel size of $3.45\times 3.45{\mu \mathrm{m}}^2$ ($2448\times 2050\text{pixels}$) and the maximum frame rate of 10 fps captured the holograms. To create a speckle-field, a diffuser was placed in the dark-field illumination path. The diffuser was being rotated by a stepper motor to produce different fields for each capturing shot. A hole in the middle of the diffuser allows the passage of the central portion of the beam that goes to the reference path, without being altered by the diffuser.

Fig. 3

Setup of a dark-field digital holographic microscope.

3.1.

Image Reconstruction

A dark-field hologram of a larva is shown in Fig. 4(a); the interference fringes can be seen in the magnified inset image. This hologram was taken using a single speckle-field illumination. An angular spectrum algorithm has been used to perform image reconstruction and digital refocusing.³⁰ Figure 4(b) shows the Fourier transform (FT) of the given hologram. One of the lobes of the first-order FT was selected (highlighted by a square) to reconstruct the intensity image [Fig. 4(c)]. Because of using the diffuser, the specimen has a random phase distribution and due to the dark background, the rest of the image shows a noisy phase distribution [Fig. 4(d)]. In addition, because of the nature of dark-field microscopy (i.e., having no light without any specimen), it is not possible to take a reference hologram and compensate for the phase contribution of the optical elements. As a result, the derived phase does not provide us with valuable quantitative information and is only used for wave-front propagation and digital focusing. To extract the 3-D profile (optical thickness) of the specimen from the phase distribution, the bright-field mode can be used. The bright-field hologram of the larva and the reconstructed phase distribution are shown in Figs. 4(e) and 4(f), respectively.

Fig. 4

(a) A dark-field hologram of a sea urchin larva taken using a single speckle-field illumination and, (b) its Fourier transform. (c) The reconstructed dark-field intensity and, (d) phase image. (e) A bright-field hologram of the same larva and, (f) the corresponding phase distribution. The inset figures in (a) and (e) shows the magnified fringe patterns in the given hologram.

3.2.

Optimal Number of Speckle Fields for Real-Time Imaging

As previously mentioned, several holograms should be captured using different speckle fields to reconstruct a high contrast intensity image. To be able to apply the technique for the imaging of living organisms, the optimal number of speckle-fields that is required to achieve a desired contrast has been evaluated. For this purpose, 100 holograms have been recorded for a given larva and the correlation between images, obtained by averaging over the different number of speckle-fields, have been plotted in two different ways. In the first case, the correlation between the image obtained from 100 speckle-fields, and the image obtained from $N$ number of fields, has been plotted [Fig. 5(a)]. From the inset figure of the plot, it can be seen that images obtained using more than 60 speckle fields have a correlation factor of more than 0.99 with the image derived from 100 fields. For the second case, the correlation between the image obtained from $N$ and ($N-1$) speckle-fields has been plotted [Fig. 5(b)]. After the 30th averaging, the correlation factor seems to follow a flat trend and, as shown in the inset figure, for 60 speckle-fields it reaches a value of 0.9996. It should be noted that to obtain a more accurate value of the correlation factor, the dark background of the images in which the specimen has no contribution, has been eliminated in the calculation. Otherwise, unrealistically high correlation factors would be obtained.

Fig. 5

(a) Correlation between the images, obtained using $N$ speckle-field illuminations, and the image, obtained using 100 speckle-fields. (b) Correlation between the images, obtained using $N$ speckle-field illuminations, and the images, obtained using $N-1$ speckle-fields. For each case, the inset figure represents a magnified appearance of the data for $N>30$.

To better demonstrate the resolution and contrast enhancement, a negative United States Air Force (USAF) test target has been utilized and the corresponding images have been presented in Fig. 6(a). The finest structure of the target, which is highlighted and magnified in the figure, has a resolution of $228\text{line-pairs}/\mathrm{mm}$. The magnified subimages, placed below the main image, were obtained by averaging over a different number of speckle-fields, indicated below each subimage. The subimages demonstrate how the image quality improves by increasing the number of speckle-fields in terms of resolution, especially compared to the case of using uniform dark-field coherent illumination [first subimage from left in Fig. 6(a)]. Summing over a given number of speckle-fields, the speckle contrast, $C$, and the signal-to-noise ratio, $S/N$, have been expressed by Goodman³¹ as,

Fig. 6

(a) The image of a negative USAF test target. The finest structure of the target, which is highlighted and magnified in the subimages, has a resolution of $228\text{line-pairs}/\mathrm{mm}$. The magnified subimages, were obtained by averaging over different number of speckle-fields, indicated below each subimage (SF: speckle-fields); including the image taken with normal illumination and introducing no speckle-field (first subimage from bottom-left). (b) The plot shows the improvement of the signal-to-noise ratio, $S/N$, (right axis) and the reduction of speckle contrast, $C$, (left axis) by increasing the number of averaging speckle fields, $N$, which has been calculated for the given USAF target.

To perform real-time imaging, the number of required holograms should be adapted to the movement speed of the specimen and the desired signal-to-noise ratio. Based on correlation factor and $S/N$ calculations, an optimal number of 60 speckle-fields or more is suggested to achieve a desirably high contrast. However, referring to Fig. 6, a fewer number of speckle-fields may be selected if the corresponding resolution and $S/N$ satisfies the requirement for a specific purpose of study. Selecting the given number of speckle-fields, $N$, the minimum required time to capture these holograms is limited to the frame rate of the camera, fps, by $N/\mathrm{fps}$.

3.3.

Digital Focusing

Due to the variant phase distribution of the diffuser for each speckle-field, the fringe pattern is different in each hologram. Therefore, it is not possible to combine all holograms at first and then perform the image reconstruction using a coherently superimposed hologram. Thus, each hologram should be analyzed separately and the corresponding intensity image should be reconstructed. The final image will be obtained by incoherent averaging over the reconstructed images. Figure 7 shows the superimposed reconstructed intensity image of the larva for different focus planes, illuminated using 60 speckle-fields. Video 1 represents the digital refocusing process for this larva. In the video, the reconstructed images were obtained from 60 speckle-fields. Sequential frames have been reconstructed by propagating the wavefront for 1 mm for each frame toward infinity. The parameter $Z$ in the video represents the axial position of the object plane relative to the initially focused plane for which the hologram has been recorded. A thin lens equation has been applied to calculate the axial position. The axial separation between the frames is limited to the depth of focus of the utilized objective (1.6 μm, according to the manufacturer information), meaning that the object layers within this distance are all in focus on the camera plane and the separation of the layers cannot be distinguished. Figure 8 and Video 2 show another two neighboring larvae in the same medium. Like Fig. 7, this figure also represents different focus planes for the given larvae. It can be seen that in each subfigure, different parts of the larva skeleton, along with the internal structure of the specimen, is in focus that results in more accurate 3-D information of the skeleton.

Fig. 7

Different focus planes for a larva with the axial position of (a) 19.9 μm, (b) 9.65 μm, (c) $-3.1\mu \mathrm{m}$, and (d) $-34.4\mu \mathrm{m}$ relative to the plane for which the hologram has been recorded. The intensity images have reconstructed using 60 sequential holograms, taken with different speckle-field illuminations.

Fig. 8

Different focus planes for two neighboring larvae with the axial position of (a) $-14.9\mu \mathrm{m}$, (b) $-22.3\mu \mathrm{m}$, (c) $-31.9\mu \mathrm{m}$, and (d) $-46.35\mu \mathrm{m}$ relative to the plane for which the hologram has been recorded. The intensity images have reconstructed using 60 sequential holograms, taken with different speckle-field illuminations.

Video 1

The video shows the digital refocusing process for a sea urchin larva immersed in water. The parameter $Z$ in the video represents the axial position of the object plane relative to the initially focused plane for which the hologram has been recorded (1.4 MB, MPG) [URL: http://dx.doi.org/10.1117/1.JBO.18.8.086009.1].

Video 2

The video shows the digital refocusing process for two neighboring sea urchin larvae immersed in water. The parameter $Z$ in the video represents the axial position of the object plane relative to the initially focused plane for which the hologram has been recorded (1.9 MB, MPG) [URL: http://dx.doi.org/10.1117/1.JBO.18.8.086009.2].