Fast image analysis in polarization SHG microscopy

Fast image analysis in polarization SHG

microscopy.

Ivan Amat-Roldan,1 Sotiris Psilodimitrakopoulos,

1 Pablo Loza-Alvarez,

1,* and

David Artigas1,2

1ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

2Department of signal theory and communications, Universitat Politècnica de Catalunya, 08034,Spain

*[email protected]

Abstract: Pixel resolution polarization-sensitive second harmonic

generation (PSHG) imaging has been recently shown as a promising

imaging modality, by largely enhancing the capabilities of conventional

intensity-based SHG microscopy. PSHG is able to obtain structural

information from the elementary SHG active structures, which play an

important role in many biological processes. Although the technique is of

major interest, acquiring such information requires long offline processing,

even with current computers. In this paper, we present an approach based on

Fourier analysis of the anisotropy signature that allows processing the

PSHG images in less than a second in standard single core computers. This

represents a temporal improvement of several orders of magnitude

compared to conventional fitting algorithms. This opens up the possibility

for fast PSHG information with the subsequent benefit of potential use in

medical applications.

©2010 Optical Society of America

OCIS codes: (180.4315) Nonlinear microscopy; (100.2960) Image Analysis; (170.3880)

Medical and biological imaging; (180.6900) Three-dimensional microscopy; (180.0180)

Microscopy; (190.4160) Multiharmonic generation; (170.0170) Medical optics and

biotechnology.

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1. Introduction

Second harmonic generation (SHG) laser scanning microscopy is considered nowadays one of

the most promising minimally invasive, high-resolution optical techniques for clinical

applications [1]. Because of recent technological advantages in micro-endoscopes/fibers [2–4]

and laser sources [5], SHG imaging shows a great potential for clinical usage as an optical

biopsy tool [6].

Earlier, numerous studies on the SHG contrast have demonstrated that collagen, myosin,

and microtubules are effective SHG converters in tissues [1]. Consequently, biological

structures that are consisting of the above endogenous SHG sources can be imaged using

intensity-based SHG microscopy. Despite the fact that the SHG intensity is the only contrast

mechanism for generating the images, several morphological parameters can be obtained [7].

For example, by comparing the forward and epi-detected SHG signals, conclusions on the

dimensions of collagen fibrils can be obtained [8]. Other methodologies take advantage of the

characteristic striation pattern for quantitative interpretation and extraction of information in

muscles [9]. In such cases, the analysis of the sarcomere pattern was used for the study of rare

diseases, including muscular dystrophy [10] and osteogenesis imperfecta [11]. More recently,


the use of image processing based on spatial Fourier analysis has been used to infer properties

of tissue and molecules of the intensity-based SHG imaging [12]. Specifically, bidimensional

(2D) Fourier transform (FT) was used to spatially quantify the disorganization of collagen

fibres due to photo-thermal damage in porcine corneas [13]. It was found that the regularities

in fibres organization leads to an elliptical distribution in the bidimensional (2D-FT)

transformed space, whereas randomness leads to a more circular distribution [14]. Also very

recently, it was presented that additional information on collagen fibre orientation and

maximum spatial frequency can be obtained using 2D-FT in an SHG image [15]. Likewise, it

was shown that the 2D-FT can also be performed in the epi-detection [16].

In addition to the above approaches, the polarization dependency of the SHG signal

(PSHG) can also be used to generate contrast [17, 18]. In particular, due to the geometric

characteristics of local hyperpolarizability tensor β(2)

arrangement, by rotating the incoming

linear polarization (or the sample), the detected SHG signal intensity from every point

provides a characteristic modulation, often called the anisotropy or signature/fingerprint curve

[19, 20]. Such PSHG modulation can be exploited to obtain information unreachable by

intensity-based only SHG imaging [21]. For example it provides intrinsic tissue

characterization without any labeling and without using an analyzer in the detection [22–24].

In particular, in collagen, PSHG has allowed obtaining the orientation of the β(2)

dominant

axis with respect the long axis of the supramolecule, which is related to the helical pitch angle

of the polypeptide chain of the collagen triple-helix [19]. In muscle such orientation is

attributed to the α-helix of the myosin’s coiled coil (myosin tail) of thick filaments [19]. In

cultured cortical neurons this orientation coincides with the architecture of the tubulin

heterodimmers forming the axons’ microtubules [25] and in starch granules it indicates

amylopectin as the SHG active molecule [26]. To obtain such information an iteration code is

usually used [19–25]. This iteration code can be based in a fitting algorithm able to fit the

PSHG images to a biophysical model in a pixel by pixel fashion [21]. However, because of

the pixel resolution examination, a typical fitting procedure takes many hours to process one

image (~6 hrs for a 512x512 pixels image). This slow processing time drastically hampers the

use of the of PSHG methodology for clinical applications. Having a fast routine able to obtain

such parameters in a robust way might open up many new and exciting applications into life

sciences.

In this work, we present a polarization 1-D FT analysis of the anisotropy curve to retrieve

the biophysical parameters of the proposed model, referred to us as Fast Fourier Polarization

SHG (FF-PSHG) analysis, to obtain the same information as with the iteration fitting-based

procedure, but instead of hours, in a few hundreds of milliseconds using a regular processor.

Considering a PSHG image of a three dimensional data set, I(x,y,α), where x-y refer to the

spatial axis of the image and α refers to the polarization dependency of the SHG image

(anisotropy curve), this FF-PSHG analysis is performed only on the polarization axis, α, of

every pixel. This is in contrast to the spatial image processing methods using 2D-FT in the

(x,y) axis discussed above [15, 16].

To show the feasibility of this method, in section 2 we describe the theory and physical

implications of the FF-PSHG analysis. This is followed in section 3 by the experimental

demonstration of the method in biological samples, showing the capability to retrieve the

orientation of the supramolecule assembly and the hyperpolarizability tensor β(2)

dominant

axis orientation (normally related to the helical pitch angle). In this section, the capability of

the method to perform discrimination between different tissues is also demonstrated using two

different strategies. Finally, these results are followed by the conclusions.

2. Theory

The biophysical model used here (see refs [20,21,23–25]) refers to an SHG active

supramolecular assembly with cylindrical symmetry. The SHG signal dependency of such

structures on the input polarization of the fundamental beam can be written as:


2 2 2 2 2

( ) sin [2( )] [ sin ( ) cos ( )] ,SHGI C A Bφ φ α φ α φ α= − + − + − (1)

where φ and α are the orientation of the long axis of the cylinder, which we assume coincides

with the supramolecular assembly alignment, and the angle of the fundamental beam

polarization, respectively, defined with respect the lab x-axis [21]. A = I0 d31, B = I0 d33 and C

= I0 d15, where I0 is proportional to the intensity of the excitation fundamental field, and d31,

d33 and d31 are the non-zero elements of the nonlinear susceptibility tensor characterizing the

tissue under cylindrical symmetry assumption [21].

The free parameters A, B, C and φ are usually obtained by fitting the experimental SHG

images for every polarization α to Eq. (1). To do that, an iterative nonlinear algorithm is

usually utilized. However, this is a lengthy task as, depending on the size of the image, this

fitting procedure may take several hours. To speed up such process, Eq. (1) can be rewritten

in a more convenient form as a sum of cosine frequency components as follows:

0 2 4

( ) cos 2( ) cos 4( ),SHGI φ α α φ α α φ α= + − + − (2)

where a0 =C2/2 +3/8 (A

2 +B

2) +AB/4, a2 = B

2/2-A

2/2 and a4 = (A-B)

2/8 – C

2/2. Note that the

parameters φ, a0, a2 and a4 contain now the whole information relative to our biophysical

model (tensor elements). In what follows, we show that these components can be readily

obtained by our FF-PSHG analysis in an efficient manner.

As commented in the introduction, in this work we are going to perform the 1D-FT only

on the polarization axis, α as i(x,y,Ω)=FαI(x,y,α). By doing so, the Fourier transform of

Eq. (2) in a pixel, determined by (x,y), with a polarization sampling between 0° and 180°,

results in

0 2 4

( ) (0) exp( 2 ) (1 ) exp( 4 ) (2 ) . .,i i i c cα δ α φ δ α φ δ− −Ω = + Ω + Ω + (3)

where c.c. indicates complex conjugated. From Eq. (3), we can now directly retrieve the

different cosine components and therefore, extract the elements’ ratio of the second order

susceptibility tensor of our model, in a pixel by pixel fashion. Note that since in an

experiment the polarization intensity period is 180°, a sampling has therefore be considered in

the 0° to 180° range. Polarization sampling performed between 0° and 360° is in fact

reproducing the measurement twice (α is equivalent to α+180°). In this case the FF-PSHG

analysis can be used by transforming the Dirac delta into δ(2−Ω) and δ(4−Ω) respectively,

with the advantage that an immediate averaging of the two set of results (from 0° to 180° and

from 180° to 360°) is obtained. In the rest of the document, for simplicity we assume the

sampling is in the range from 0° to 180°. Note that the quadratic nature of PSHG response

[see Eq. (1)] generates a symmetric polarization response in the polarization intervals α ∈ [0,

π], therefore φ has the same periodicity, which for convenience we chose the range φ ∈ [- π/2,

π/2].

Before go further, it is worth to note that Eq. (1) possesses a mathematical intrinsic

ambiguity that affects any PSHG experiment. This ambiguity is apparent when the same

result is obtained by exchanging A and B and adding π/2 phase to the orientation φ [21]. From

a physical point of view, this ambiguity appears because the model is build in a manner that

assumes a minimum SHG signal when the incident polarization is perpendicular to the

cylinder’s long axis. Experimentally, this has been reported to occur in several biosamples

such as microtubulin of axons [25], collagen [18] or starch [26], and results in B/C >A/C ≈1.

However, muscle [20] shows the minimum SHG signal when the incident polarization is

parallel to the thick filaments orientation (assumed to posses the cylindrical symmetry), with

B/C <A/C ≈1. Since the ambiguity cannot be solved using mathematical criteria, a priori

knowledge on the different sample PSHG response was needed. When using the fitting

algorithm, the ambiguity is solved in every pixel by assigning the value closer to the unity to


A/C. Then if this value is associated to the sinus in Eq. (1) the orientation is directly the

retrieved angle φ. On the contrary, if A/C is associated to the cosine in Eq. (1), the actual

orientation isφ+π/2.

2.1. Determining the orientation of the supramolecular assembly φ

The above ambiguity also affects our FF-PSHG analysis, particularly in the orientation φ.

Direct observation of Eq. (2) shows that φ only affects the cosine argument. Therefore, when

performing Fourier transform to Eq. (3), it will appear as a phase in the first and second

(second and four) coefficients when performing the sampling between 0° and 180° (0° and

360°). Then, the extraction of the orientation φ consists in computing the complex argument

of the second coefficient as

2' arg[ exp( 2 )] / 2iφ α φ= (4)

In Eq. (4), the ambiguity is apparent in the fact that the obtained angle φ' and the

orientation φ can be different, since φ' also include information on the sign of a2. This is

because a2 = B2/2-A

2/2 can either be positive (|B|>|A|) or negative (|B|<|A|). This unknown

sign is transformed in the intrinsic ambiguity of π/2 in calculating the angle orientation φ. This

is totally equivalent to the ambiguity in Eq. (1) by exchanging A and B and adding π/2 to the

orientation φ [21]. Similarly, the condition used with iterative fitting algorithms, |A/C|<|B/C|,

results in a2>a4, characteristic of collagen and starch, while |A/C|>|B/C| results in a2<a4,

which is typical in myosin. Therefore, by comparing a2 and a4 it is possible to solve the

indetermination as follows:

2 2 4

2 2 4

' for

' 2 for

a a

a a

φφ

φ π

≥=

+ <

(5)

For other tissues it will be possible to design different strategies and define specific

criteria. Also note that since the extraction of φ.is based on the phase of the polarization-

spectral components, it is, in principle, independent of possible errors affecting the amplitudes

a0, a2 and a4, adding robustness to the method.

2.2. Extraction of the biophysical parameters

The rest of the parameters, A, B and C can be then extracted analytically by combining Eqs.

(1) and (2) as:

2

0 2 4

2

0 2 4

2

0 4

2/ 2 / 2)( ,

A

B

C A B

α α α

α α α

α α

= +

= ± +

= +− −

∓

(6)

Where the change of sign in Eq. (6) is related to the discussed ambiguity, and must be chosen

accordingly to the criteria used in selecting the cylinder’s orientation, φ. Once these three

parameters have been computed, the tensor element ratios can be calculated as d31/ d15=A/C

and d33/d15=B/C. This can be performed in an almost instantaneous way (considering the

current speed of modern computers) with no constrains.

Once this is done, it is possible to go a step forward and calculate the angle θe between the

hyperpolarizability tensor β(2)

dominant axis (the nonlinear SHG-dipole, normally related to

the helical pitch angle) and the long axis of the supramolecular assemble . To do that, a series

of restrictions, related with or in addition to the “single-axis molecule” approach, are normally

imposed: (1) there is only one major orientation φ in each pixel, (2) the long axis of the

supramolecular assemble is parallel to the imaging plane (2D), (3) both Kleinman and

cylindrical symmetries hold. All these conditions imply that A=C, or equivalently, d31/ d15=1.


However, any deviation from the above restriction, experimental errors and detection noise

level, resulted in a certain distribution around d31/ d15=1 [21, 23, 25, 26]. In this situation, the

algorithm can be forced to fulfill A=C by considering a0 =A/2 +3/8 (A2 +B

2) +AB/4, a2 =

B2/2-A

2/2 and a4 = (A + B)

2/8 – A/, and use only one of the two equations in (6) to determine

A and B. Then, the results of d33/ d15, or alternatively A and B can be used to obtain θe as [21–

23,25,26]:

2

cos / (2 ).e

B A Bθ = + (7)

2.3. Pixels with erroneous results

In previous works, we have shown the capability of the iterative algorithms to remove pixels

with erroneous results by filtering them out by setting a threshold on the fitting coefficient of

determination, r2 (usually keeping pixels presented r

2 > 90%) [21,23,25,26]. Here we propose

a different strategy that is based on the analysis of the spectral components for the PSHG

modulation response.

The source of noise in the PSHG images includes experimental errors like anisotropy of

the sample, depolarization introduced by the optical components, optical misalignment, non-

exact determination of the polarization, saturation and poor signal to noise ratio (SNR). This

means that the noise within a pixel can be considered being equally distributed among all the

spectral components obtained after performing the 1D-FF in the polarization axis. Among all

these components, only those with Ω ≤ 2 have biophysical meaning according to current

model [see. Eq. (3)].. Therefore, the origin of any signal appearing in polarization frequency

components with Ω > 2 can be associated to noise. As result, since FF-PSHG analysis only

uses the spectral components Ω ≤ 2, noise associated to the components with Ω > 2 is

intrinsically filtered in determining all the previous parameters.

In addition to this filtering, the noise at components Ω > 2 can be used to estimate the total

amount of error in the coefficients a0, a2 and a4. To do that, we assume that the error in the

frequency components at Ω = 0, 1 and 2 (related with a0, a2 and a4) is affected in a similar

way as those components with Ω > 2. Therefore the experimental error in determining a0, a2

and a4 in a pixel can be estimated comparing the spectral components as

0 2 4

( , ) [ ( ( , , ), 2)] / [ ( , , )]e x y mean i x y mean α α α= Ω Ω > (8)

For example, the signal detected in pixels in areas outside any SHG active tissue is noise

in nature and therefore results in a value of e ≈1. However, pixels in areas with a good signal

to noise ratio will result in e ≈0. Then, since e quantifies the error in a pixel, it can be used to

filter out pixels with e above a certain threshold value, eth, which are considered erroneous

[i.e., do not match Eqs. (1)–(3)]. Typical values for the threshold are in the range eth ≈0.02-

0.1.

3 Results-discussion

In this section, we show the capability of determining the orientation of the supramolecular

assembly φ, also referred as fiber orientation, discussing the ambiguity described in

subsection 2.1, and the determination of θe. This is followed by two methods to perform

discrimination among tissues.

3.1 Single SHG-active structure images

To show the ability of the algorithm to locally determine the orientation of the supramolecular

assembly we analyze a representative case: a granule of starch. A granule of starch has been

previously reported to possess a radial molecular orientation [26]. This sample is ideal to

show the performance of the method since it allows obtaining data within the whole

orientation range, from 0° to 180°. The multiphoton microscope used to acquire the PSHG


images has been thoroughly described in Refs [21,23,25,26]. The linear polarization at the

sample plane exhibited an extinction ratio of 25:1. By comparing the summed reconstruction

of linear polarization images with the image created using circular polarization, we found this

ratio adequate. Figure 1 shows the results, measuring the angle φ using both the FF-PSHG

analysis, which is obtained in 100 ms, and a fitting algorithm, which lasted ~6 hours with 400

iterations per pixel. The results are very similar, clearly retrieving the radial-like structure.

The small deviation of the radial symmetry in Fig. 1 might be attributed to the imperfections

on the starch granule. We can also observe that a smooth change from pixel to pixel is

obtained with FF-PSHG analysis, without the need of pixel averaging, as is the case in the

image obtained with the iterative algorithm. We attribute this smooth variation to the filtering

process intrinsic in the FF-PSHG analysis. In addition to this filtering procedure, pixels with e

> 0.05 have been removed from the image (black color). Notice that only points near the

external surface of the starch granule disappears, denoting the quality of the measurement. In

the case of the fitting algorithm, pixels with coefficient of determination r2<90%, has been

filtered out. Finally, when using a fitting algorithm, final results slight change depending on

the initial conditions and number of iterations. This is not the case in our FF-PSHG analysis,

since its analytical nature always provides the same results. This adds robustness and

consistency to the analysis.

Fig. 1. Calculation of fiber orientationφ in starch: (a) Mean SHG intensity of the 9 PSHG

images. Scale bar shows 10µm. (b) FF-PSHG analysis using 9 polarizations and (c) iterative

fitting algorithm using 8 polarizations.

We next analyze the capability of the method to clearly determine changes in the φ

orientation by using a more sophisticated sample. Figure 2(a) shows a detail on the orientation

for a collagen fiber shown later in Fig. 4. In this figure we have manually delineated the

orientation of the fiber (white line), computing the angle at every point of the line. This result,

shown in Fig. 2(b), is then compared with the angle retrieved at selected pixels of the curve

using our FF-PSHG analysis. A nice agreement is observed, showing consistency of the

method that is able to calculate angular deformations. This result entails us to use this method

to analyze complex fiber situations as shown in Fig. 2(c). Again, an image showing a smooth

variation of the fiber orientations is obtained.


Fig. 2. (a) detail of fiber of collagen and manual delineation of fiber trajectory in white and (b)

comparison of local PSHG fiber orientation (solid) and angle of the manual delineation

(dashed); and retrieved fiber orientation using the FF-PSHG analysis is shown in (c). Pixels

with e > 0.1 have been filtered out and are represented in black pseudocolor.

With the above results, the reliability of the method to determine any fiber orientation

change is clearly demonstrated. This allows analyze complicated situations and go a step

forward to obtain the helical pitch angle in a sample, with pixel resolution, and compare the

results obtained with the fitting algorithm and the FF-PSHG analysis. The results,

corresponding to bundle of collagen fibers oriented in different directions, are showed in Fig.

3 (the corresponding fiber orientation is shown in Fig. 2c). Figure 3(a) shows the

superposition of the SHG intensity images for all the polarizations. This figure show the

difficulties to obtain SHG signal in some areas, specifically in most of the points in the top

part of the collagen bundle that will result in a poor noise to signal ratio. As a consequence,

the analysis performed using the iterative algorithm, shown in Fig. 3(b), lacks important parts

of the image, which has been filtered out due to the low quality of fitting in the top part of the

image (points with coefficient of determination, r2<85% where removed). In spite of the

decrease of useful pixel, the fitting algorithm is able to correctly retrieve the helical pitch

angle, whose distribution is shown in Fig. 3(c), with the maximum frequency at θe = 44.4° and

a distribution width of ∆θe = 5.4° (the helical pitch angle obtained with X-ray diffraction

measurements is ~45°). On the contrary, the FF-PSHG analysis shown in figure Fig. 3(d) is

able to map θe in the entire sample, even for those areas with low SHG signal quality (notice

the top part of the bundle of collagen fibers). This is possible to the noise filtering intrinsic to

the method. The image shows smooth changes that give the impression of volume, which

correlates well with the contour of Fig. 3(a). This makes us suspect that the variation in θe can

be attributed to be mainly produced by out of plane fiber axis orientations. The θe frequency

distribution obtained with the FF-PSHG analysis is shown in Fig. 3(e), showing a

displacement of the maximum, at θe = 42.3° and a distribution width of ∆θe = 4.9°. This

displacement of the maximum is attributed to major number of pixels with θe ≈40°, appearing

in the top part of the bundle of collagen fibers, which are filtered out by the fitting algorithm

in Fig. 3(c).

Regarding the time required to compute the above Figs. 2-3 (500 x 500 pixels), the FF-

PSHG analysis lasted around 100 ms to compute the fiber orientation, while the calculus of θe


required less than 300 ms. Figures obtained with the fitting algorithm, where obtained with

400 iterations per pixel and lasted ~6 hours.

Fig. 3. Lyophilized Achilles’ tendon collagen. (a) Superposition of the SHG intensity images

for eight polarizations. Scale bar shows 10µm. (b) Image showing the helical pitch angle in

every pixel obtained using an iterative fitting algorithm and its frequency distribution in (c).

Similarly, (d) shows the helical pitch angle in every pixel and its frequency distribution in (e),

this time using the FF-PSHG analysis.

3.2 Multiple SHG-active structure images

PSHG offers the unique characteristic of identifying and discriminating different SHG active

molecules, with pixel resolution, in the same image [23]. In this section we show that our FF-

PSHG analysis can also be used with discrimination purposes by computing B/A parameter

and θe in every pixel [using Eq. (7)]. The results for unstained temporalis muscle from rat are

shown in Fig. 4(a), where it is possible to observe a clear discrimination between two tissues,

orange corresponding to muscle and blue to collagen. In this case, the time required to

compute Fig. 4(a) was less than 300 ms.

In addition to the discrimination method described above, the FF-PSHG analysis offers a

simple discrimination alternative based on directly mapping the cosine frequency components

a0, a2 and a4 into RGB images. Since the values of a0, a2 and a4 depend on the actual SHG

molecule, the weight for every RGB channel is different for different tissues. Therefore,

different tissues appear with different pseudocolor in the same image. The results are shown

in Fig. 4(b). We can observe that both tissues are clearly differentiated. In order to identify

what are the actual tissues displayed, the typical relation among values a0, a2 and a4 must be

characterized. In the case of Fig. 4(b), and by comparing with Fig. 4(a), in the RGB

representation yellow corresponds to collagen and purple to myosin. This provides a simple

method to discriminate among different tissues, getting an instantaneous perception of the

image, with the advantage that the time required to compute Fig. 4(b) was less than 100 ms, in

a single core computer, after acquiring the corresponding PSHG data.

Comparing Figs. 4(a) and 4(b), we see that both methods provide similar discrimination

capabilities, the main difference being the image appearance. This differences in the images

appears because the cosine frequency components a0, a2 and a4 contains information on the

ratio among a0, a2 and a4, which is always the same for a tissue (providing the discrimination

capability), and on the intensity, providing smoother changes in the image. This results in an


apparent better quality of Fig. 4(b) when compared with Fig. 4(a). However, although the

RGB representation provides the fastest method to discriminate between different SHG

sources, the standard method has the advantage that the tissue identification is based on a

known intrinsic characteristic of the SHG active molecule, as is the helical pitch angle,

providing a clear criterion in case of ambiguous situations. This is clearly apparent when

plotting the frequency distribution for the helical pitch angle as showed in Fig. 4(c). The two

well separated, not overlapping peaks centered at 43° and 64° for collagen and muscle,

respectively, show the ability of the method to unambiguously distinguish between tissues in

the same image.

Fig. 4. (a) Map of the computed helical pitch angle using FF-PSHG (b) Pseudocolored cosine

coefficients a0, a2 and a4 of Eq. (2), plotted into RGB images, red channel is a0, green channel

is a2 and blue channel is a4. Scale bar shows 10µm, and (c) the helical pitch angle frequency

distribution of Fig. 3(a), exhibiting a centre of the distribution at 43° for collagen and 64° for

myosin.

4. Conclusions

Polarization-sensitive Second Harmonic Generation is a promising imaging modality that

enables statistically studying the orientational distribution of the β(2)

dominant axis (related to

the helical pitch angle) of a number of molecules which play a role in many biological

processes: collagen, microtubulin and myosin and additional structures, like starch, which has

been also used to probe polarization state in a microscope [27]. Especially when optical

clearing is used, this information can be acquired several hundreds of microns deep in tissues

[28]. Therefore, many applications can be enhanced by the development of new and faster

algorithms than the current ones, which are executed “offline”, requiring from minutes to

hours to process an image of 500 by 500 pixels, even with multi-core computers.

In this paper, we have presented for the first time an approach that allows processing in

few milliseconds an image based on 1D Fourier analysis of the PSHG modulation response

obtaining a temporal improvement of near five orders of magnitude. This opens the possibility

for PSHG imaging to penetrate new fields in medicine at video rates, acting for example as an

instantaneous diagnostic supporting method in surgery. The results are in total agreement of

those obtained by conventional fitting algorithms, where the intrinsic noise filtering results in

a smother response and a better contrast, while its analytical nature provides robustness and

consistency to the analysis. In conclusion, we have presented a sub-second method to process

PSHG images to extract full biophysical meaning and straight visualization methods that can

be useful for many fields in microscopy and biomedicine that possess additional advantages

that do not possess its prior competitors.

Acknowledgments

This work is supported by the Generalitat de Catalunya grant 2009-SGR-159 and by the

Spanish government grant TEC2009-09698 Authors also acknowledge the Laserlab-Europe


Cont (JRA4: Optobio 212025) and the Photonics4Life networks of excellence. This research

has been partially supported by Fundació Cellex Barcelona.


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Fast image analysis in polarization SHG microscopy

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