3. Quantitative phase imaging for sperm analysis

#### 3.1. Basic principles of quantitative phase microscopy

stress and corroborated the findings using an established assay and an alternative but complementary spectroscopic technique (Fourier-transform infrared (FTIR) spectroscopy). The results of this last work confirm that RS is able to reveal different levels of oxidative DNA fragmentation, especially associated to alterations within the 1050–1095 cm�<sup>1</sup> spectral range (Raman spectra in the box 2 of Figure 2), which includes the band associated with the DNA phosphate backbone, changes that were confirmed by similar shifts in the corresponding FTIR peaks (not shown) [25]. Also, the Raman bands associated to protein and lipid content (1400–1600 cm�<sup>1</sup>

solely on the presence of differing spectra [24].

224 Spermatozoa - Facts and Perspectives

Figure 2. Overview of the most representative studies on Raman spectroscopy and imaging for the label-free analysis of sperm cells. Box 1: the highlighted variations in peak intensities in the Raman spectra correspond to different sperm head shapes [21]. Box 2: the peaks at 1095 and 1050 cm�<sup>1</sup> represent biomarkers of fragmented DNA in the sperm nucleus [24, 25]. Box 3: panel A shows the chemical Raman reconstruction of distinct sperm regions [23]; panels B–Y represent the biochemical composition of individual immobilized, living human sperm cells [26]; and panel Z shows the efficiency of Raman imaging in revealing small irregularities in the sperm head such as vacuoles (yellow circles) distinguishable based

showed some alterations induced by UV radiation, consistent with protein denaturation and lipid peroxidation that are well-known markers of oxidative damage [27]. Raman-based identification of DNA-damaged sperm cells linearly correlated with the findings from the flow

)

Quantitative phase microscopy (QPM) is a label-free imaging technique, which allows reconstructing both the amplitude and the phase information of an optical field that passes through the sample, and it is particularly interesting in case of transparent biological cells. Respect to differential interference contrast (DIC) microscopy [29] or Nomarski/Zernike's phase contrast [30], the QPM gives a quantitative measure of the optical path difference (OPD) at each point in the sample. OPD in each position (x, y) of the acquisition plane is defined as the refractive index variation across the cell thickness, t(x, y):

$$\text{OPD}(\mathbf{x}, \mathbf{y}) = t(\mathbf{x}, \mathbf{y})(n\_c - n\_s) \tag{2}$$

where nc and ns are the refractive index of the cell and the surrounding medium (assumed to be homogeneous), respectively. The resulting OPD map of the cell is reconstructed by recording the interference fringes pattern, the so called "hologram," of two superimposed coherent beams, one that interacts with an object under test and another that does not come in contact with the object and acts as a reference beam, and calculating the phase difference between them [31]. If the hologram is acquired by a digital sensor array, typically a charge-coupled device (CCD) or a complementary metal-oxide semiconductor (CMOS) device, digital holographic microscopy (DHM) technique is implemented. A typical interferometric setup for DHM is reported in Figure 3.

The acquired hologram is then mathematically analyzed, allowing obtaining the complex field of the object beam that can be reconstructed at different distances, too. Therefore, numerical refocusing of a digital hologram, that is a 2D image, at different object planes, without any zscan of the optical system, allows to retrieve a 3D quantitative imaging [31]. This makes digital holography a very powerful method for metrology applications, particularly attractive in the field of biology as it is noninvasive, noncontact, and label-free, allowing the characterization of live specimen.

Intensity and phase distributions can be reconstructed by Sprop(m, n) according to the following

Ipropð Þ¼ <sup>m</sup>; <sup>n</sup> Spropð Þ <sup>m</sup>; <sup>n</sup>

The phase φprop(m, n) includes information about the morphological profile of the object under

λ

Digital holography (DH) allows retrieving a fully 3D image of the sample, thus offering new prospects for the analysis of sperm cells in a noninvasive, quantitative, and label-free way. Sperm cells were acquired by a digital holographic microscope for the first time in 2008 by

The potential of applying this technique for label-free sperm assessment was recently confirmed by Shaked's group. Indeed, they demonstrated that DHM allows obtaining equivalent information about key morphological parameters of fixed human spermatozoa to that

Additionally, the opportunity to have information about the third dimension in the sperm analysis can offer a better understanding of this kind of cell and of male infertility [40]. Furthermore, since this technique allows obtaining quantitative information and numerical analysis, estimation area or profiles in a given direction may be carried out. Such kind of analysis can help to study the male infertility and its possible relation with the abnormal

DH has been mainly employed to study the morphology of human sperm cells in order to verify the integrity of their structures and to evaluate their kinematic parameters and concentration. This approach allows to visualize the morphology of abnormal sperm and to analyze in 3D some typical defects such as cytoplasmic droplet along the tail, bent tail, and acrosome

Additionally, a quantitative study of vacuoles has been performed by DH. In particular, it was demonstrated that the profile of the normal spermatozoon results higher than that of the spermatozoon with vacuoles, whereas their 2D dimensions (such as area and axes length) are similar [43]. The difference in height denotes a reduced volume in spermatozoon with vacuoles respect to the normal spermatozoon; this difference could be ascribed to a modification of the

inner structure of the sperm head with loss of material (see box 1 in Figure 4).

φpropð Þ¼ m; n arctan

OPD mð Þ¼ ; n

The relation between the OPD and the thickness of the cell t is given by Eq. (2).

obtained by bright field microscopy (BFM) imaging of stained sperm cells [39].

3.2. Digital holography microscopy for sperm cells assessment

investigation; in fact, it is related to the OPD:

 2

Advanced Label-Free Optical Methods for Spermatozoa Quality Assessment and Selection

Im Spropð Þ <sup>m</sup>; <sup>n</sup>

; (5)

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227

Re Spropð Þ <sup>m</sup>; <sup>n</sup> : (6)

<sup>2</sup>πφpropð Þ <sup>m</sup>; <sup>n</sup> : (7)

equations:

Mico et al. [38].

morphology [41, 42].

broken, as reported in the box 1 of Figure 4 [42].

Figure 3. Typical interferometric setup for digital holography microscopy. BS: beam splitter, M: mirror. Reference and object beams are highlighted.

In DHM, in addition to the hologram of the sample under investigation, a second hologram is acquired on a reference region near to the object in order to numerically compensate all the aberrations due to the optical components, comprising the defocusing due to the microscope objective. An "off-axis" configuration is generally adopted to avoid a spatial overlapping of the real and conjugate images due to the holographic reconstruction, leading to the separation of first diffraction order from the entire spatial frequency spectrum. Thus, the spectrum of the sample (object field defined as S(x, y)=|S(x, y)|e iφ(x, y) , with |S(x, y)| and φ(x, y) amplitude and phase, respectively) can be retrieved except for a constant [32]. Then, it is possible to propagate the optical wavefront at different distances from the plane of acquisition applying the Fourier formulation of the Fresnel-Kirchhoff diffraction formula [33, 34]. This reconstruction can be obtained by means of the operator algebra proposed by J. Shamir [35], where Fresnel diffraction is described by replacing the Fresnel-Kirchhoff integral, the lens transfer factor, and other operations by operators. The resulting propagated object field Sprop(ξ, η) is expressed as a function of the initial object field S(x, y) and can be written as [36, 37]:

$$\mathcal{S}\_{\text{pr}\mathfrak{p}}(\nu,\mu) = \exp\left(\text{ikd}\right) \times \left\{ \Im^{-1} \left[ \exp\left(-\frac{\text{ik} d\lambda^2}{2} \left(p^2 + q^2\right)\right) \right] \Im(\mathbf{S}(\mathbf{x},y)) \right\} \tag{3}$$

being <sup>I</sup>½ � f xð Þ the Fourier transform of the function <sup>f</sup>(x), <sup>k</sup> <sup>¼</sup> <sup>2</sup>π<sup>n</sup> <sup>λ</sup> (with n refractive index of the medium), <sup>p</sup> and <sup>q</sup> spatial frequencies defined as <sup>p</sup> <sup>¼</sup> <sup>ν</sup> <sup>λ</sup><sup>d</sup> and <sup>q</sup> <sup>¼</sup> <sup>μ</sup> <sup>λ</sup><sup>d</sup>, and d the reconstruction distance. For digital reconstruction, Eq. (3) is applied in a discrete form:

$$\mathcal{S}\_{prop}(m,n) = \exp\left(i\hbar d\right) \left\{ \mathfrak{I}\_D^{-1} \left[ -\frac{i\hbar d\lambda^2}{2N^2 d^2} (\mathcal{U}^2 + V^2) \right] \mathfrak{I}\_D(S(h,j)) \right\} \tag{4}$$

where N is the number of pixels in both directions and m, n, U, V, h, and j are integer numbers varying from 0 to N � 1.

Intensity and phase distributions can be reconstructed by Sprop(m, n) according to the following equations:

$$I\_{prop}(m,n) = \left| S\_{prop}(m,n) \right|^2; \tag{5}$$

$$\varphi\_{prop}(m,n) = \arctan \frac{\text{Im}\left[\mathcal{S}\_{prop}(m,n)\right]}{\text{Re}\left[\mathcal{S}\_{prop}(m,n)\right]}.\tag{6}$$

The phase φprop(m, n) includes information about the morphological profile of the object under investigation; in fact, it is related to the OPD:

$$\text{OPD}(m,n) = \frac{\lambda}{2\pi} \varphi\_{pmp}(m,n). \tag{7}$$

The relation between the OPD and the thickness of the cell t is given by Eq. (2).

#### 3.2. Digital holography microscopy for sperm cells assessment

In DHM, in addition to the hologram of the sample under investigation, a second hologram is acquired on a reference region near to the object in order to numerically compensate all the aberrations due to the optical components, comprising the defocusing due to the microscope objective. An "off-axis" configuration is generally adopted to avoid a spatial overlapping of the real and conjugate images due to the holographic reconstruction, leading to the separation of first diffraction order from the entire spatial frequency spectrum. Thus, the spectrum of the

Figure 3. Typical interferometric setup for digital holography microscopy. BS: beam splitter, M: mirror. Reference and

iφ(x, y)

<sup>2</sup> <sup>p</sup><sup>2</sup> <sup>þ</sup> <sup>q</sup><sup>2</sup>

<sup>d</sup><sup>2</sup> <sup>U</sup><sup>2</sup> <sup>þ</sup> <sup>V</sup><sup>2</sup>

<sup>λ</sup><sup>d</sup> and <sup>q</sup> <sup>¼</sup> <sup>μ</sup>

phase, respectively) can be retrieved except for a constant [32]. Then, it is possible to propagate the optical wavefront at different distances from the plane of acquisition applying the Fourier formulation of the Fresnel-Kirchhoff diffraction formula [33, 34]. This reconstruction can be obtained by means of the operator algebra proposed by J. Shamir [35], where Fresnel diffraction is described by replacing the Fresnel-Kirchhoff integral, the lens transfer factor, and other operations by operators. The resulting propagated object field Sprop(ξ, η) is expressed as a

> <sup>D</sup> � ikdλ<sup>2</sup> 2N<sup>2</sup>

where N is the number of pixels in both directions and m, n, U, V, h, and j are integer numbers

, with |S(x, y)| and φ(x, y) amplitude and

∙Ið Þ S xð Þ ; y

∙IDð Þ S hð Þ ; j

<sup>λ</sup> (with n refractive index of the

<sup>λ</sup><sup>d</sup>, and d the reconstruction

(3)

(4)

sample (object field defined as S(x, y)=|S(x, y)|e

object beams are highlighted.

226 Spermatozoa - Facts and Perspectives

function of the initial object field S(x, y) and can be written as [36, 37]:

Sprop <sup>ν</sup>; <sup>μ</sup> <sup>¼</sup> exp ð Þ� ikd <sup>I</sup>�<sup>1</sup> exp � ikdλ<sup>2</sup>

distance. For digital reconstruction, Eq. (3) is applied in a discrete form:

being <sup>I</sup>½ � f xð Þ the Fourier transform of the function <sup>f</sup>(x), <sup>k</sup> <sup>¼</sup> <sup>2</sup>π<sup>n</sup>

Spropð Þ¼ <sup>m</sup>; <sup>n</sup> exp ð Þ ikd <sup>I</sup>�<sup>1</sup>

medium), <sup>p</sup> and <sup>q</sup> spatial frequencies defined as <sup>p</sup> <sup>¼</sup> <sup>ν</sup>

varying from 0 to N � 1.

Digital holography (DH) allows retrieving a fully 3D image of the sample, thus offering new prospects for the analysis of sperm cells in a noninvasive, quantitative, and label-free way. Sperm cells were acquired by a digital holographic microscope for the first time in 2008 by Mico et al. [38].

The potential of applying this technique for label-free sperm assessment was recently confirmed by Shaked's group. Indeed, they demonstrated that DHM allows obtaining equivalent information about key morphological parameters of fixed human spermatozoa to that obtained by bright field microscopy (BFM) imaging of stained sperm cells [39].

Additionally, the opportunity to have information about the third dimension in the sperm analysis can offer a better understanding of this kind of cell and of male infertility [40]. Furthermore, since this technique allows obtaining quantitative information and numerical analysis, estimation area or profiles in a given direction may be carried out. Such kind of analysis can help to study the male infertility and its possible relation with the abnormal morphology [41, 42].

DH has been mainly employed to study the morphology of human sperm cells in order to verify the integrity of their structures and to evaluate their kinematic parameters and concentration. This approach allows to visualize the morphology of abnormal sperm and to analyze in 3D some typical defects such as cytoplasmic droplet along the tail, bent tail, and acrosome broken, as reported in the box 1 of Figure 4 [42].

Additionally, a quantitative study of vacuoles has been performed by DH. In particular, it was demonstrated that the profile of the normal spermatozoon results higher than that of the spermatozoon with vacuoles, whereas their 2D dimensions (such as area and axes length) are similar [43]. The difference in height denotes a reduced volume in spermatozoon with vacuoles respect to the normal spermatozoon; this difference could be ascribed to a modification of the inner structure of the sperm head with loss of material (see box 1 in Figure 4).

the OPD of the cell linearly depends on the axially averaged refractive index of the cell relative to the surrounding medium, for a given thickness t [45]. Thus, considering that the human spermatozoa head can be divided in the cell nucleus and the acrosome, which differ in the composition and concentration of proteins, nucleic acids, and other components, Balberg et al. evaluated the dry mass of the cell by starting by the knowledge of the OPD [31]. In particular, the authors measured the dry mass of separate cellular compartments in the OPD maps of

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229

Finally, the movements of living spermatozoa have been tracked applying an automatic 4D tracking (movements in the 3D spatial directions over time) of the swimming samples in [46]. The results are showed in the box 3 of Figure 4, where an anomalous spermatozoa behavior, known as "bent tail," is highlighted. A collection of several holograms at a fixed distance between the sample and the microscope objective was acquired. In order to simultaneously track multiple spermatozoa, a proximity criterion has been included into the algorithm. In particular, by means of this approach, the position in the (n + 1)th frame has been searched in a

Therefore, DH could be seen as a breakthrough that can renew the sperm analysis in the spermatology laboratories, encouraging researchers in the field of sperm cell biology to con-

As seen in the previous sections, Raman spectroscopy and quantitative phase microscopies have been separately developed for assessing spermatozoa from a biochemical and morphological perspective, respectively. The two photonic techniques, employing intrinsic contrast mechanisms, allow noninvasively selecting the fertile spermatozoon according to its normal morphology as well as its DNA integrity. Kang et al. [47] first proposed a combined system where quantitative phase microscopy and Raman imaging allowed correlating morphological parameters with molecular information, i.e. the red blood cell thickness was correlated to the hemoglobin distribution. Huang and colleagues in 2014 published a study that evaluated the possibility to combine micro-Raman spectroscopy with image analysis for label-free identification of normal spermatozoa [48]. Recently, our group proposed a similar system, which combines Raman spectroscopy/imaging and digital holography microscopy as a potential tool

The setup used in our works for the simultaneous Raman and holographic analysis essentially consists of a Raman microscope coupled to an interferometer (Figure 5) [36, 49, 50]. We used two different laser sources: a green laser at 532 nm for the Raman excitation and a long coherence (>100 m) red laser at 660 nm for the holographic experiments. The red laser beam was split into two beams: the object beam passing through the sample and the reference beam

4. Combined optical approach for the noninvasive analysis of single

unlabeled human spermatozoa, as reported in the box 2 of Figure 4.

sider using DH as a standard method for their characterization studies.

to rapidly and objectively identify the healthy spermatozoa [36, 49, 50].

reasonable neighborhood of the nth frame position.

spermatozoa

4.1. The optical setup

Figure 4. Some potentialities of DHM. Box 1: morphological analysis of semen carried out by DHM; top panels: sperm cells with distinct morphological defects; center and bottom panels: difference in height denotes a reduced volume in spermatozoon head with vacuoles respect to the normal spermatozoon [41, 43]. Box 2: examples of some physical parameters obtained by DHM [31, 44]. Box 3: 4D tracking of clinical sperm samples [45].

In 2013, Merola et al. [44] provided an evaluation of the biovolume of spermatozoa (about 55 μm<sup>3</sup> ). The authors used optical tweezers to trap and rotate the cells; meanwhile, they flow through a microchannel, enabling recording digital holograms of the sperm at different angles and the production of a tomographic 3D model, as showed in the box 2 of Figure 4.

Another important semen parameter, the dry mass of the cell (i.e. the average mass of the proteins, carbohydrates, lipids, and so on within the cell), can be obtained by DHM. Indeed, the OPD of the cell linearly depends on the axially averaged refractive index of the cell relative to the surrounding medium, for a given thickness t [45]. Thus, considering that the human spermatozoa head can be divided in the cell nucleus and the acrosome, which differ in the composition and concentration of proteins, nucleic acids, and other components, Balberg et al. evaluated the dry mass of the cell by starting by the knowledge of the OPD [31]. In particular, the authors measured the dry mass of separate cellular compartments in the OPD maps of unlabeled human spermatozoa, as reported in the box 2 of Figure 4.

Finally, the movements of living spermatozoa have been tracked applying an automatic 4D tracking (movements in the 3D spatial directions over time) of the swimming samples in [46]. The results are showed in the box 3 of Figure 4, where an anomalous spermatozoa behavior, known as "bent tail," is highlighted. A collection of several holograms at a fixed distance between the sample and the microscope objective was acquired. In order to simultaneously track multiple spermatozoa, a proximity criterion has been included into the algorithm. In particular, by means of this approach, the position in the (n + 1)th frame has been searched in a reasonable neighborhood of the nth frame position.

Therefore, DH could be seen as a breakthrough that can renew the sperm analysis in the spermatology laboratories, encouraging researchers in the field of sperm cell biology to consider using DH as a standard method for their characterization studies.
