Time-gated ballistic imaging using a large aperture switching beam.

Time-gated ballistic imaging using a large aperture switching beam Florian Mathieu, Manuel A. Reddemann, Johannes Palmer, and Reinhold Kneer∗ Institute of Heat and Mass Transfer, RWTH Aachen University, 52056 Aachen, Germany ∗ [email protected]

Abstract: Ballistic imaging commonly denotes the formation of lineof-sight shadowgraphs through turbid media by suppression of multiply scattered photons. The technique relies on a femtosecond laser acting as light source for the images and as switch for an optical Kerr gate that separates ballistic photons from multiply scattered ones. The achievable image resolution is one major limitation for the investigation of small objects. In this study, practical influences on the optical Kerr gate and image quality are discussed theoretically and experimentally applying a switching beam with large aperture (D = 19 mm). It is shown how switching pulse energy and synchronization of switching and imaging pulse in the Kerr cell influence the gate’s transmission. Image quality of ballistic imaging and standard shadowgraphy is evaluated and compared, showing that the present ballistic imaging setup is advantageous for optical densities in the range of 8 < OD < 13. Owing to the spatial transmission characteristics of the optical Kerr gate, a rectangular aperture stop is formed, which leads to different resolution limits for vertical and horizontal structures in the object. Furthermore, it is reported how to convert the ballistic imaging setup into a schlieren-type system with an optical schlieren edge. © 2014 Optical Society of America OCIS codes: (110.0113) Imaging through turbid media; (140.7090) Ultrafast lasers; (190.3270) Kerr effect; (110.1220) Apertures.

References and links 1. L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991). 2. R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Yici Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, and W. B. Wang, “Time-resolved and nonlinear optical imaging for medical applications,” Ann. N. Y. Acad. Sci. 838, 14–28 (1998). 3. M. Paciaroni and M. Linne, “Single-shot, two-dimensional ballistic imaging through scattering media,” Appl. Opt. 43(26), 5100–5109 (2004). 4. M. Paciaroni, Time-gated Ballistic Imaging Through Scattering Media with Applications to Liquid Spray Combustion (Ph.D. thesis, Division of Engineering, Colorado School of Mines, 2004). 5. M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40(6), 836–846 (2006). 6. M. Linne, M. Paciaroni, E. Berrocal, and D. Sedarsky, “Ballistic imaging of liquid breakup processes in dense sprays,” Proc. Comb. Inst. 32(2), 2147–2161 (2009). 7. D. Sedarsky, Ballistic Imaging of Transient Phenomena in Turbid Media (Ph.D. thesis, Division of Combustion Physics, Lund University, 2009). 8. M. Linne, D. Sedarsky, T. Meyer, J. Gord, and C. Carter, “Ballistic imaging in the near field of an effervescent spray,” Exp. Fluids 49(4), 911–923 (2009).

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Received 29 Oct 2013; revised 18 Jan 2014; accepted 31 Jan 2014; published 19 Mar 2014 24 March 2014 | Vol. 22, No. 6 | DOI:10.1364/OE.22.007058 | OPTICS EXPRESS 7058

9. D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express 19(3), 1866–1883 (2011). 10. S. Idlahcen, L. Méès, C. Rozé, T. Girasole, and J.-B. Blaisot, “Time gate, optical layout, and wavelength effects on ballistic imaging,” J. Opt. Soc. Am. A 26(9), 1995–2004 (2009). 11. K. Sala and M. C. Richardson, “Optical Kerr effect induced by ultrashort laser pulses,” Phys. Rev. A 12(3), 1036–1047 (1975). 12. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20(5), 2170–2187 (1979). 13. A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, Toluene, Benzene, and Carbon Disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94(9), 6167–6174 (2003). 14. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, 2006). 15. D. Sedarsky, M. Paciaroni, J. Zelina, and M. Linne, “Near field fluid structure analysis for jets in crossflow with ballistic imaging,” 20th ILASS Americas, Chicago, IL (2007). 16. C. Torres-Torres, A. V. Khomenko, L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Measurements of nonlinear optical refraction and absorption in an amino-triazole push-pull derivative by a vectorial self-diffraction method,” Opt. Commun. 281(12), 3369–3374 (2008). 17. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer, 2001). 18. E. Hecht, Optics, 4th ed. (Addison Wesley Longman, 2002). 19. R. R. Alfano (ed.), Semiconductors Probed by Ultrafast Laser Spectroscopy, Volume II (Academic, 1984). 20. E. R. Ippen and C. V. Shank, “Picosecond response of a high-repetition-rate CS2 optical Kerr gate,” Appl. Phys. Lett. 26(3), 92–93 (1974).

1.

Introduction

Ballistic imaging is a shadowgraphy technique that was proposed for imaging transient structures hidden in optically dense media. Initially it was investigated as medical diagnostic method for imaging through human tissue (see e.g. [1, 2]) but in recent years its applicability for spray research was also analyzed by a number of studies [3–8]. Despite this effort, ballistic imaging cannot yet be recognized as a turn-key imaging technique for sprays, since it incorporates a number of complex phenomena whose interaction has to be precisely controlled: A femtosecond laser is commonly used to provide ultrashort light pulses that act as illumination source for the images and as switch for the optical Kerr gate, an optically triggered shutter. Since the gate has to be integrated into the imaging path, ballistic imaging requires specific design of the imaging path with respect to the imaging conditions. Besides classical design targets like magnification, field of view or resolution limit, also the scattering conditions influence the imaging system. For example Sedarsky et al. [9] compared two imaging setups for different sizes of scatterers forming the turbid medium. Their results indicate that an optimized imaging system for small scattering particles may be poorly suited for larger scatterers and vice versa. This example emphasizes that there are numerous aspects that have to be considered in order to acquire high-quality images. The scope of this study is to investigate the influence of a large aperture switching beam (D = 19 mm) that triggers the optical Kerr gate. The basic idea is to increase the resolution limit of the imaging system by increasing its numerical aperture. In order to provide sufficient electric fields for switching the gate, a high-amplified femtosecond laser capable of pulse energies up to ≈ 25 mJ and pulse durations down to ≈ 40 fs is used. The experimental results are analyzed by means of calculations of the spatial and temporal transmission characteristics of the optical Kerr gate using the approach by Idlahcen et al. [10]. Finally, a comparison of acquired images using ballistic imaging as well as standard shadowgraphy is conducted and the modulation transfer functions are evaluated to judge the advantages of either technique.

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2.

Theory and simulation

A number of questions have to be addressed when setting up imaging path and optical Kerr gate. In this section three aspects will be discussed theoretically: i) how does spatial overlap between imaging and switching beam influence transmission as this is of particular importance for a large aperture switching beam, ii) what pulse energy and duration are necessary to achieve maximum transmission and a sufficiently short shutter and iii) how should the optical Kerr gate be positioned relative to the imaging lenses. 2.1.

Optical Kerr gate

An optical Kerr gate consists of a Kerr cell embedded between two crossed polarizers as shown in Fig. 1. Two light pulses interact in the Kerr cell: the switching beam induces birefringence in the Kerr fluid (here: carbon disulfide) and the imaging beam probes this birefringence and experiences a phase shift allowing passage of the second polarizer.

polarizer (P2)

x

45° z

y polarizer (P1) 45°

imaging pulse

ll r ce Ker s

switching pulse

r Fig. 1. Sketch of an optical Kerr gate with axes definition used in this study.

Substances with a notable Kerr effect become birefringent when exposed to an electric field. The substance then behaves like an uniaxial crystal with the optical axis parallel to the electric field. In case a short laser pulse is used to provide the electrical field, the induced difference in refractive indices parallel and perpendicular to the electric field Δn = n − n⊥ is given by e.g. Sala and Richardson [11] and is extended by introducing spatial dependencies: Δne = Δne + Δno

2 1 t − s/v r 2 e e 2 e 2 · exp −2 Δn = n2 E (r,t) = · n2 E0 · exp − 2 τl R √ π τl τl 2 t − s/v t − s/v r 2 o o 2 τl Δn = n2 E0 · erfc · exp − − · exp −2 τo 4 2τo τl 2τo τo R

(1) (2) (3)

In contrast to the model of Idlahcen et al. [10], which also considers spatial dependencies, the induced birefringence is split into an electronic contribution Δne , which covers the instant response of the Kerr medium to the electric field, and an orientational contribution Δno , which covers the slow response due to molecular orientation [3, 11, 12]. The temporal characteristics of the orientational contribution are described by the molecular relaxation time τo of the Kerr #200378 - $15.00 USD (C) 2014 OSA


medium. The electric field is represented by its peak amplitude E0 and the pulse shape is assumed to be Gaussian both in time and space (t, r). The laser pulse duration is√included via τl , which relates to the commonly used pulse width at half maximum as τp = 2τl · ln 2. R denotes the pulse radius (intensity decay to 1/e2 ). In the given form, the pulse propagates along the s-axis with velocity v. Assuming monochromatic light, the induced phase shift Δφ experienced by the imaging pulse traveling a cell along x with thickness L is: Δφ =

L 2π 0

λ

· Δn(x) · dx

(4)

Malus’ law finally yields the overall transmittance T of the optical Kerr gate. Here, θ denotes the angle between the polarization state of the incident light (optical axis of the first polarizer) and the optical axis of the Kerr cell: IT 2 Δφ · sin2 (2θ ) (5) T = = sin I0 2 For optimum performance of the optical Kerr gate, the pulses should be arranged so that θ = 45◦ . Furthermore, in the experimental part of this study, the polarization state of the switching pulse is aligned along the z-axis, thus being collinear with the extraordinary field component of the imaging pulse, which precludes a potential double image due to birefringence. An ideal optical Kerr gate would induce a constant phase shift in the imaging pulse of Δφ = π acting like a zero-order half-wave plate while the switching pulse is present and would immediately stop changing the imaging pulse polarization after the switching pulse has passed. As can be seen from theory, numerous influences control the real behavior of the optical Kerr gate: Pulse duration, energy and size, substance properties of the Kerr liquid and furthermore the overlap of both pulses characterized by the propagation axes x and s or their intersection angle respectively. To gain a physical understanding of the temporal and spatial behavior of the gate, the induced phase shift is calculated using a discretization scheme illustrated by Idlahcen et al. [10]. The calculations require knowledge of the pulse envelope’s velocity v, which is the group velocity given by Eq. (6). v=

c n − λ ∂∂λn

= 1.809 · 108 m/s

(6)

The dispersion terms are calculated with Cauchy’s equation according to Samoc [13]. The peak electric field amplitude E0 , which is not directly accessible by experiments, is expressed in measurable quantities, i.e. the pulse energy W , the pulse cross-sectional area Acs and the pulse duration τp . The linkage of these quantities can be estimated for a Gaussian pulse by (compare e.g. [14]): √

ε0 cn π 2 · E0 · τp · Acs I(r,t) · dt · dA = √ (7) W= 8 ln 2 A t

One drawback of the employed low-repetition (10 Hz) laser in contrast to commonly used kHz-systems is its worse stability in terms of pulse energy and pulse duration. During the experiments the fluctuations were measured to be in the range of ±5 % for both pulse energy and duration. Hence, in a first step the effect of these fluctuations on the theoretical transmission of the gate is calculated without accounting for spatial dependencies (r = s = 0). Figure 2 shows the induced phase shift and the corresponding transmission of the optical Kerr gate calculated with parameters adapted from the following experiments. The electronic contribution to the phase shift follows the switching pulse envelope instantly, whereas the molecular contribution is delayed. After the pulse has passed, the phase shift does not drop to zero but decays slowly #200378 - $15.00 USD (C) 2014 OSA


Temporal Response of Opcal Kerr Gate 1.0 Δφe Δφo Δφtot T error

4/3 π

π 2/3 π 1/3 π

0.1

0.8 0.6 0.4

transmission

phase shi / rad

5/3 π

0.2 1

me / ps

10

Fig. 2. Calculated temporal behavior of phase shift experienced by the imaging pulse and transmission of the optical Kerr gate according to Eqs. (1–5) neglecting spatial dependencies. Δφ e : electronic contribution to phase shift, Δφ o : molecular contribution to phase shift, Δφtot = Δφ e + Δφ o . Calculation parameters: E0 = 2.231 · 108 V/m, τl = 42 fs, λ = 800 nm, θ = 45 ◦ , L = 10 mm. Error bars were computed assuming fluctuations in pulse energy and pulse duration of 5 %.

due to the slow reorientation of the CS2 -molecules. Owing to the periodic nature of Eq. (5) the transmittance of the optical Kerr gate is oscillating since the maximum phase shift in this case exceeds π . Accordingly, a further increase in the electric field would lead to more oscillations in the early stage but the usable transmission window of the gate is characterized by the last decay in the transmission trend. The width of this time window is in the range of the relaxation time of the Kerr medium (τgate ≈ τ0 = 2 ps). Since Eq. (5) is ill-conditioned for Δφ = π + 2π k, the aforementioned superimposed fluctuations in energy and pulse duration lead to strong fluctuations of ±50 % in transmission. Accounting for spatial dependencies, the computation of the presented theory requires temporal discretization and spatial discretization of the Kerr cell. The basic procedure is given by Idlahcen et al. [10]. To validate the correct implementation of the employed discretization scheme, the analytical solution of the aforementioned case from Fig. 2 was compared to the discretized solution with an intersection angle between imaging and switching beam of α = 0 ◦ . The computational error was below 1 % when choosing a temporal discretization Δt < 0.25 · τl , which was taken as temporal resolution criterion for the following calculations. Figure 3 shows the simulated phase shift distribution that imaging light has experienced after passing the Kerr cell drawing an angle of α = 18.8 ◦ with the switching pulse direction. The region of notable phase shift in the y − t−plane is inclined by n·v/sin(α ), since the physical overlap angle in the cell is smaller than α due to refraction. Furthermore, the angle leads to a considerable drop of phase shift: although the electric field amplitude and the pulse duration have been kept constant compared to Fig. 2, the peak phase shift drops from 4.9 to 1.3 rad when considering the angle. The radial behavior of the Kerr gate is of particular importance for the design of the imaging optics and the positioning of the optical Kerr gate in the imaging path. In Fig. 3, an imaging pulse can be represented by a horizontal line whose thickness corresponds to its pulse duration and whose length (extent in y-direction) is controlled by the imaging optics. Apparently the radial extent of the imaging pulse has to be minimized in the Kerr cell if a homogeneous phase shift across the whole field of view is pursued. This finding is emphasized by Fig. 4(a), which shows radial profiles of the induced phase shift for various time steps. With increasing delay of the imaging pulse the experienced phase shift moves radially from right

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Spaal and Temporal Phase Shi / rad 70

5/

12 π

4/

12 π

55

65 me / ps

detail (1 mm x 6 ps) 57

60

53 3/12 π

55

-0.25

0

0.25 2/

arbitrary imaging pulse

50

45 peak phase shi: 1.3 rad inclinaon: n·v/sin α = 0.9 mm/ps 40 -10 -5 0 5 Kerr cell cross coordinate (y) / mm

1/

12 π

12 π

10

Fig. 3. Spatial and temporal behavior of phase shift experienced by an imaging pulse according to Eqs. (1–5). The drawn horizontal line represents an arbitrary imaging pulse which experiences a phase shift only from y = 1.5 to 5.5 mm (phase shift profiles given in Fig. 4(a). Calculation parameters: E0 = 2.231 · 108 V/m, R = 9.5 mm, τl = 42 fs, α = 18.8 ◦ , λ = 800 nm, θ = 45 ◦ , L = 10 mm, n = 1.6056. (also compare [10])

to left. The profiles show a steep slope at the left edge whereas a slight decay is present on the right side. To characterize these profiles, their radial width at half maximum is evaluated together with their peak value for each time step, see Fig. 4(b). The width increases with time and reaches values around ΔyFWHM ≈ 1.7 mm at maximum phase shift.

1/

3π

1/

6π

49 ps 51 ps 53 ps 55 ps 57 ps

a)

Δφpeak ΔyFWHM

5 b) 4 3 2 1

-5 0 5 radial coordinate (y) / mm

45

50 55 me / ps

ΔyFWHM / mm

phase shi / rad

1/2 π

60

Fig. 4. Spatial phase shift behavior derived from simulation. a) Induced phase shift in radial direction for various synchronization timings between imaging and switching pulse, b) peak phase shift Δφpeak (left ordinate) as function of synchronization timing and width at half maximum of the radial profiles ΔyFWHM (right ordinate).

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2.2.

Image formation

The term ’ballistic imaging’ might lead to the assumption that the image formation exclusively relies on ballistic photons. This assumption is incorrect since diffracted light cannot be distinguished from ballistic photons and a simple projection of light onto a screen without optics suffers from diffraction. Hence, image formation in ’ballistic imaging’ relies on classical imaging optics collecting at least partly scattered light from the object. For this reason the number of possible setups of the imaging optics is infinite, as for standard imaging tasks. Nonetheless, in literature mainly one setup has been used for ballistic imaging. It is called 1f-system [3–6,8,15], which indicates that the first lens is placed one focal length away from the object. As mentioned before, Sedarsky et al. [9] have recently shown that an alternative 2f-system is advantageous for imaging through turbid media composed of large scatterers (≈ 15 µm), which generally better suits real technical conditions such as sprays, but in this study a 1f-system is used mainly for two reasons: i) it is simple because only two lenses are used and ii) it is flexible since the positioning of the optical Kerr gate between those two lenses is not critical for the imaging system itself. The general setup is shown in Fig. 5.

obj

L1

stop

L2

ima

D

f1

f1

f2

variable

Fig. 5. Imaging setup and optical path of the 1f-system. The magnification of the system is M = − f2/ f1 .

Since the object is placed in the front focal plane of the first lens all rays emerging from one object point propagate parallel after the first lens. At this position the gate optics themselves theoretically do not introduce optical path differences in the imaging rays. Furthermore, the space between both lenses for inserting the optical Kerr gate is variable with only slight concessions regarding the field of view. Figure 6 quantifies the induced aberrations of the imaging system including the optical Kerr gate. The rays emerging from both selected object points experience optical path differences below 0.3 λ across the entire entrance pupil. The optics works diffraction limited.

opcal path diﬀerence

0.5 λ

object point

785 nm 800 nm 815 nm

0.5 λ

object point -0.5 λ

normalized pupil coordinate

-0.5 λ

Fig. 6. Optical path differences at the image plane for the 1f-system from Fig. 5 including polarizers and Kerr cell calculated with a commercial ray-trace code.

However, as was seen in section 2.1 the position of the Kerr cell is bound to the position of

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the aperture stop (one focal length behind the first lens, i.e. the Fourier plane of the first lens), if one does not accept severe deformation of field of view. This constitutes a major design restriction for the imaging path as the first lens’ focal length has to be selected with respect to physical space for the first polarizer and the incoupling mirror of the switching pulse. Given the present equipment it was possible to achieve angles down to α ≥ 15 ◦ for f1 ≥ 100 mm. A far more important restriction regarding the resolution is given by the stop size D determined by the optical Kerr gate. The smallest resolvable structure Δlmin can be estimated by: Δlmin = 1.22λ ·

f1 D

(8)

Assuming an ideal Kerr cell, the resolution is limited by the aperture of the gate’s polarizers (here: D = 20 mm). The introduction of a real Kerr cell must influence stop size because the cell cannot induce a homogeneous phase shift over the full aperture, recall Fig. 4. Hence for a 1f-system the resolution of ballistic imaging is necessarily lower than that of standard shadowgraphy with the same optical path. This is true for the radial direction (y), since the Kerr gate acts like a rectangular slit being narrow primarily in y-direction. The decrease in resolution can be estimated by comparison of the stop sizes according to Table 1. Table 1. Stop sizes D and diffraction limits Δlmin for the 1f-system employing the first lens (L1) with clear aperture of 23 mm and focal length f1 of 150 mm. Stop sizes for the Kerr cell are derived from simulation and thus denote their extent in y-direction (Fig. 4).

D/mm Δlmin /µm

system

+polarizers

+Kerr cell

23 6.3

20 7.3

≈ 1.5 to 3 ≈ 49 to 98

In summary it should be pointed out that the scope of ballistic imaging is not to increase resolution but to image structures larger than resolution limit through turbid media. Nonetheless one has to bear in mind the decrease of resolution when analyzing ballistic images in particular when high optical magnifications are set up. 3. 3.1.

Experiments Turbid medium

As commonly used in other studies, suspensions of polystyrene spheres in water are employed to provide turbid media. A reference target (USAF 1951) with line pairs of various spatial frequencies was placed inside the suspension and acted as object. The optical thickness OD of the suspension is defined by the light transmission in forward direction T according to Beer’s law: (9) OD = μ · l = − ln(T ) The scattering coefficient μ is a function of sphere concentration csusp in the suspension and l denotes the path length of light travelling the turbid medium. The transmission was measured using a spectrometer detecting the irradiance from an 800 nm-cw-laser before and after a suspension. The measured relation for average sphere diameters of 549 nm is:

μ = 13.346

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l · csusp g · cm

(10)


3.2.

Ballistic imaging setup

A sketch of the ballistic imaging setup is given in Fig. 7 and the entire equipment used is summarized in Table 2 (section 5.1). The femtosecond amplifier is capable of producing pulses with energies of up to 25 mJ and durations of down to 40 fs with a spectral band of 800 ± 15 nm. The beam diameter at the output port is 19 mm. Pulse energy and pulse duration can be controlled by a wave-plate polarizer combination and a motorized delay-stage in the compressor stage of the amplifier.

BD O L1

KC

P1

M

BP P2 L2 SP

EMCCD

imaging pulse

α switching pulse

M

M M

DS

M LP laser

M ½WP ND

PBS

½WP

Fig. 7. Experimental setup: the femtosecond pulse is initially split into imaging and switching pulse before they overlap in the Kerr cell with a characteristic angle α . The image is formed by two lenses (L1 and L2) surrounding the optical Kerr gate that consists of the Kerr Cell (KC) placed between two crossed polarizers (P1, P2).

After exiting the laser, a pulse passes a combination of half-wave plate and polarizing beam splitter (½WP, PBS) that allows for variable splitting ratios of switching and imaging pulse. The portion reflected by the beam splitter is vertically polarized and marks the switching pulse. It passes a longpass filter (LP) before being directed to the Kerr cell (KC). The delay stage (DS) is used to precisely adjust the temporal overlap of imaging and switching pulse inside the Kerr cell. The longpass filter is included to prevent scattered switching light from the Kerr cell to propagate to the CCD of the camera, which is therefore protected by a shortpass filter (SP). The portion transmitted by the beam splitter is horizontally polarized and marks the imaging pulse. It passes an optional set of neutral density filters (ND) to decrease the irradiation in the image plane as necessary. The second half-wave plate rotates the polarization of the imaging pulse by an angle of 45◦ so that it is coincident with the first polarizer’s axis (P1). Then the imaging pulse is directed to the object. The achromatic doublets (L1 and L2) are arranged as 1f-system and form the final image. The optical Kerr gate (P1, KC, P2) is placed between them. The camera is not equipped with a further lens but the image is directly projected onto the CCD by the second achromatic doublet (L2). In order to reject all ambient light, a tube equipped with a bandpass filter (BP) is mounted onto the camera. To measure the pulse duration, additional mirrors were introduced at points of interest to guide the pulse to a single-shot autocorrelator.

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3.3. 3.3.1.

Results Transmission of the optical Kerr gate

In a first step, the transmission of the optical Kerr gate was tested without imaging optics and collimated imaging pulse (L1, L2 removed). Figure 8 shows the acquired images of the transmitted pulse without switching, Fig. 8(a), and at different timings of switching and imaging pulse, Figs. 8(b)–8(d). A qualitative comparison of the transmission windows between experiment and simulation is also given. transmission / a.u.

experiment simulaon

a)

b)

c)

d)

y / mm -3

0

3

-3

0

3

-3

0

3

-3

0

3

Fig. 8. Images of the transmitted pulse and related transmission curves without imaging optics. a) Cross section of raw pulse with both gate polarizers being parallel (no switching). b) An early imaging pulse at time step t0 leads to transmission at the edge of the Kerr cell. Delaying the imaging pulse, c) t0 + 4.7 ps, d) t0 + 7.3 ps, leads to transmission windows crossing the Kerr cell. Governing parameters according to Fig. 3.

As can be seen, experiment and simulation are in good qualitative agreement considering the sharp rise on one flank and the slow decay on the other flank of the transmission window. The width of these windows is slightly underestimated by the simulations as well as the inclination (depicted in Fig. 3). Both is likely due to group velocity dispersion, which not only affects pulse velocity but also leads to pulse broadening. Referring to section 2.2, this experiment verifies the presence of a spatially distorted aperture of the optical Kerr gate. Regarding quantitative comparisons, the acquired data suffers from the laser’s high amplification: this not only comes along with pulse energy and duration fluctuations in the range of 5 % but also introduces fluctuations in the spatial intensity profile, which affects the Kerr gate notably. Nonetheless, transmission is also investigated quantitatively with respect to varying switching beam setups. Figure 9(a) shows measured temporal transmission profiles for three different switching pulse energies. The profiles for 4.6 and 2.8 mJ feature distinct drops at ≈ 3.7 ps, which indicates that the maximum phase shift has exceeded π under these conditions. This is supported by simulation of the 4.6 mJ case. The data points around the drops show high standard deviations, which indicates that Eq. 5 is ill-conditioned for Δφ = π + 2π k. The reason why 100 % transmission could not be reached in the experiments is unclear. As mentioned before, spatial distortions of the switching pulse together with fluctuations of the electric field will influence transmission, but also further effects cannot be excluded, for instance losses in the Kerr cell due to self-diffraction (compare [16]). Comparing different switching setups with varying #200378 - $15.00 USD (C) 2014 OSA


overlap angles in Fig. 9(b) shows that the qualitative trend of the experiments is predicted satisfyingly by the simulations: both, experiment and simulation indicate an increase of phase shift with decreasing overlap angle α and increasing switching beam energy. It is noteworthy that experiment and simulation are in fairly good quantitative agreement for a comparatively low switching beam energy of 1.1 mJ. This is likely due to less severe non-linear effects such as pulse broadening or self-phase modulation: in fact observance of the spatial intensity profile of the switching pulse showed fewer distortions when decreasing switching beam energy. In summary, it is desirable to reduce α as much as possible, as this reduces both, the necessary switching beam energy and hence the occurrence of unwanted non-linear effects.

b) peak transmission a) temporal transmission overlap angle: α = 19°

switching pulse energy 1.1 mJ 2.8 mJ 4.6 mJ

bars: exp. dots: sim.

transmission / %

100 4.6 mJ (sim.) 4.6 mJ (exp.) 2.8 mJ (exp.) 1.1 mJ (exp.)

80 60 40 20 0 2

4

6

8 me / ps

19°

30° 45° overlap angle: α

Fig. 9. Comparison of experimental and simulated transmission of the optical Kerr gate: a) temporal transmission profiles, b) peak values of the temporal profiles for various switching beam energies and intersection angles α . The error bars mark standard deviations of measured data from 50 consecutive repetitions.

3.3.2.

Imaging characteristics

As pointed out in section 2.2 an advantage of ballistic imaging over standard shadowgraphy can only be expected at high optical densities of the turbid medium. This is emphasized by analyzing acquired images without turbid medium as shown in Fig. 10. Standard shadowgraphs are taken with the Kerr gate’s polarizers turned into transmitting position and without switching pulse. To gain a quantitative comparison the modulation transfer function (MTF) was evaluated according to Imax − Imin C( f ) , where: C( f ) = . (11) MTF = Cref Imax + Imin The reference contrast Cref was determined as the contrast of the lowest spatial frequency in the image, i.e. Cref = C (4 lp/mm). The MTF was evaluated for horizontal and vertical lines respectively and it turns out that there is a distinct difference for both directions. For the standard shadowgraphs the MTF’s do not drop below 30 % over the investigated frequency range, but at high spatial frequencies the contrast of vertical lines is clearly lower than that of horizontal lines: this difference was found to be caused by the Kerr cell windows, which are not ideally flat but slightly curved and hence act as cylindrical lens. Consequently this effect varies notably between different cells due to their tolerances in production. One measure to minimize this influence is minimizing the distance between Kerr cell and image plane to restrict deviation of rays to the minimum possible. The MTF of the switched image reveals poorer contrast throughout the frequency range compared to the standard shadowgraphs. Contrasts of vertical

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line pairs again are lower than those of their horizontal counterparts. The cut-off frequency for vertical structures is ≈ 22 lp/mm, for horizontal ones it is ≈ 40 lp/mm. This difference cannot be explained by the cell windows exclusively, but by the deviating resolution limits due to directional stop sizes discussed in section 2.2. Vertical structures are blurred due to diffraction at the comparatively small radial aperture of the Kerr gate.

standard

switched

standard, horizontal standard, vercal

switched, horizontal switched, vercal 1

Modulaon Transfer Funcon 10

20 30 40 spaal frequency / lp/mm

50

0

Fig. 10. Comparison of standard (no switching) and switched shadowgraph of the test target through pure water (no turbid medium).

Figure 11 shows acquired images of the resolution test target for selected optical densities of the turbid media and compares ballistic and standard shadowgraphs. As expected, for standard shadowgraphs contrast decreases with increasing optical density; for optical densities greater than 10 it was not possible to image the object with the standard setup. Here, the images (upper row) reveal that multiply scattered photons illuminate the CCD even at locations where dark structures should be visible; while the dark lines are still visible at OD = 10, they vanish beyond a bright homogeneous background at OD = 12. On the other hand ballistic images (lower row) show a much more stable contrast for optical densities up to 10, because multiply scattered photons are largely removed. Therefore, the object is still visible at OD = 12.

OD = 10

OD = 12

ballisc

standard

OD = 8

Fig. 11. Images of the test target for various turbid media.

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In Fig. 12 the imaging performance is quantified by derived MTF’s of both setups. The analysis of imaging performance through turbid media is restricted to horizontal structures only. As already indicated by the images, contrast and hence cut-off frequency continuously decrease with increasing optical density for the standard setup. At low optical densities the MTF’s of the ballistic images show poorer performance than their standard counterparts but the profiles are much more stable for OD ≤ 10 with cut-off frequencies in the vicinity of ≈ 35 lp/mm. Increasing the optical density above 10 finally leads to an abrupt decrease of contrast also for the ballistic setup. Nonetheless, the potential of ballistic imaging is apparent at OD = 12: while the image could not be formed with the standard setup, ballistic imaging is capable of revealing structures with low spatial frequencies under these circumstances.

MTF for standard shadowgraphs

MTF for ballisc shadowgraphs

1 OD = 0 OD = 5.8 OD = 10 OD = 12

0

10


50

10


50

Fig. 12. Influence of optical density (OD) on image contrast for standard and ballistic shadowgraphs

In summary, the present ballistic imaging setup shows advantages over standard shadowgraphy when imaging through turbid media with optical densities of 8 < OD < 13. 3.3.3.

Optical schlieren edge

When setting up the ballistic imaging technique, it is a priori not possible to determine an absolute value for the temporal synchronization of imaging and switching pulse. Hence it is unknown how the delay stage (DS in Fig. 7) should be adjusted to overlap both pulses in the best possible way. Therefore, the delay stage is continuously adjusted and the transmitted images are monitored simultaneously. Figure 13 shows such an image sequence with Fig. 13(a) as reference image acquired through transmitting polarizers without switching. Figure 13(b) is a schlieren image, again acquired through transmitting polarizers: the schlieren effect is achieved by inserting a vertical knife edge in the focal plane of the first imaging lens so that half of the imaging path is cut off (see e.g. [17, 18]). Figures 13(c)–13(h) are acquired through crossed polarizers by means of the optical Kerr gate. Besides the expected fade-in and fade-out of the target’s image, Figs. 13(f) and 13(g) reveal the same modulation as the schlieren image. Here only intensity gradients in horizontal direction cause light to propagate onto the CCD. However, in the setup described here, there is no solid edge present, apparently the edge is purely optical and is formed by the sharp-edged transmission band according to Fig. 4(a), which is in fact placed in the focus of the first imaging lens, i.e. the position of the Kerr cell. For ballistic imaging using a large aperture switching beam this implies two sides of one coin: ballistic imaging can be used to perform standard shadowgraphy as well as schlierentype shadowgraphy in one setup, but in order to gain reliable results one has to clearly separate schlieren from standard shadowgraphs, because the identification and analysis of objects and structures requires knowledge whether a count level of the CCD was caused by light intensity

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a)

b)

c)

d)

e)

f)

g)

h)

Fig. 13. Image sequence of the resolution test target for different synchronization timings: a) reference image (no switching), b) schlieren image (no switching, vertical knife edge inserted), c) transmitted image by Kerr switching at t0 and transmitted images for continuously delayed switching pulses: d) t0 − 2.7 ps, e) t0 − 6 ps, f) t0 − 6.7 ps, g) t0 − 7.3 ps, h) t0 − 8.7 ps.

or by a light intensity gradient. 4.

Summary and outlook

The commonly used explicit model to describe phase shift in an optical Kerr gate covering spatial dependencies is employed to study the influences of overlap angle, switching beam energy and fluctuations of the electric field. The governing Eq. (5) is ill-conditioned for π < Δφ < 3π so that laser pulse fluctuations in energy and duration of ±5 % lead to transmission fluctuations of up to ±50 % indicating that laser stability is a prerequisite for a stable optical Kerr gate. Depending on the switching beam energy, theory predicts oscillation of the temporal transmission profile, which could be reproduced experimentally by transmission measurements of the optical Kerr gate. The spatial phase shift distribution emphasizes the importance of focusing the imaging beam into the cell to establish uniform transmittance across the field of view. Especially when using a large aperture switching beam, the overlap angle should be minimized for efficient switching for two reasons: i) given a certain electric field transmission increases with decreasing angle and ii) the described distortion of the aperture stop is less severe for shallower angles. One restriction of minimizing the angle is scattering at the Kerr cell windows: the shallower the angle the more scattered switching light propagates from the cell windows towards the CCD. Although the current setup uses color separation and the CCD is equipped with a filter blocking switching light, collinear propagation of imaging and switching beam is prevented by scattered switching light using standard filters. The spatial phase shift distribution also influences imaging quality. The Kerr cell transmission constitutes a distorted non-circular aperture, which is narrow in radial direction (y-axis in Fig. 1) and as broad as the switching beam diameter in perpendicular direction (z-axis in Fig. 1). This directly leads to differing resolutions for horizontal and vertical structures in the image. Cut-off frequencies of the modulation transfer function (MTF) without turbid medium are evaluated as ≈ 22 lp/mm (horizontal line pairs) and ≈ 40 lp/mm (vertical line pairs). This at least partly contradicts the basic idea of using a large aperture switching beam, because an #200378 - $15.00 USD (C) 2014 OSA


increase of numerical aperture could only be achieved in one (vertical) direction. Reference experiments were carried out by imaging a resolution test target placed in suspensions of polystyrene spheres and water. The optical path of the 1-f system is designed with a commercial ray trace code yielding a diffraction-limited imaging path. The comparison of ballistic images to standard shadowgraphs shows that the present ballistic imaging setup is advantageous over standard shadowgraphy for optical densities in the range 8 < OD < 13. For lower optical densities, scattering in the turbid medium does not degrade standard images notably, for higher optical densities an image could not be acquired even with ballistic imaging. In this context, it will be interesting to address the question how overall imaging pulse energy influences the advantageous OD-range for ballistic imaging. All images in this study represent the best shot that could be acquired (here, up to ≈ 10 mJ for the imaging pulse were available), and it is assumed that the advantageous OD-range changes depending on the available imaging energy. During setup of optimum synchronization between imaging and switching pulse, images of the test target were taken that exhibit a schlieren-type modulation. Since the aperture of the optical Kerr gate features a steep edge on one side, the Kerr gate acts as an optical schlieren edge. Counts of the CCD are then caused by intensity gradients perpendicular to the edge rather than by illumination in the object plane. Judging the applied theory to model the optical Kerr gate, it should be pointed out that various influences have not been considered that might be of interest for future research: i) non-linear effects induced by the extremely high electric fields of the pulses such as pulse broadening, self-phase modulation or self-focusing, ii) thermal effects due to continuous pumping of the Kerr cell influencing the non-linear refractive index of the Kerr fluid or, iii) the potential of self-diffraction in the Kerr cell, which might lead to considerable losses in the optical Kerr gate (see e.g. [16]). Furthermore, the utilized theory makes use of the slowly varying envelope approximation (SVEA), which must be questioned when opting for a more precise theoretical description. Nonetheless, although quantitative agreement between experiment and simulation suffered from distortions of the spatial intensity distribution of the switching pulse especially at high switching pulse energies, the present model proved to be appropriate for understanding the optical Kerr effect qualitatively and for explaining the presented experimental results. 5. 5.1.

Appendix Listing of equipment Table 2: Part listing of the setup shown in Fig. 7, which was used in this study unless otherwise noted. symbol Laser

½WP PBS ND M O

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description / vendor femtosecond amplifier, Coherent: Hidra-25-USP (Seedlaser: Coherent: Mantis, Pumplaser: Innolas Spitlight 600) pulse energy: 25 mJ, pulse duration: 40 fs, repetition rate: 10 Hz, center wavelength: 800 nm, bandwidth: 30 nm half-wave plate, CVI Melles Griot: QWPO-800-10-2 polarizing beam splitter cube, CVI Melles Griot: PBSK-700-900-100 neutral density filter, Newport: FSQ-OD100...300 mirror, CVI Melles Griot: TLMB-800-45-2037 object cell, Hellma Analytics: 700.002-OG polystyrene particles, Microparticles GmbH: PS-F-0.55 resolution test target, Thorlabs: R1DS1P


symbol

description / vendor

L1 L2 P1 / P2

achromatic lens, CVI Melles Griot: LAO-150.0-25.0 (f = 150 mm) achromatic lens, Newport: PAC091 (f = 500 mm) Glan-laser polarizer, CVI Melles Griot: 03PLS305/C extinction ratio: 5 · 105 : 1 cylindrical Kerr cell, Starna: 35 H 10 (non-birefringent fused silica) carbon disulfide (CS2 ), Sigma-Aldrich: 180173 shortpass filter, Thorlabs: FES0800 longpass filter, Thorlabs: FEL0800 bandpass filter, Thorlabs: FB800-40 delay stage, CVI Melles Griot: 07TXC727/A electron multiplying CCD-camera, Andor: iXon+ 888 (1024x1024 pixel, 13 µm/pixel)

KC SP LP BP DS EMCCD

5.2.

Nomenclature

Acs c csusp C D E(r,t) E0 f I(r,t) I0 , IT Imax , Imin l Δlmin L n Δn ne2 , no2 OD r R s t Δt T v W x y ΔyFWHM z α

cross sectional area of switching pulse, [m2 ] velocity of light in vacuum: 2.998 · 108 m/s sphere concentration in the suspension: [g/l] image contrast, [−] stop size, [mm] amplitude of the electric field, [V/m] peak amplitude of the electric field, [V/m] focal length, [m] intensity distribution of a laser pulse I(r,t) = ε0 cnE 2 (r,t), [W/m2 ] incident and transmitted intensity, [W/m2 ] maximum and minimum intensity, [W/m2 ] path length through the turbid medium, [cm] resolution limit, [µm] Kerr cell thickness, [m] refractive index, carbon disulfide at 800 nm (from [13]): 1.6056 induced birefringence in the Kerr cell, [−] electronic and orientational contribution to non-linear refraction: from [3, 19]: ne2 = 2.114 · 10−21 m2/V2 , no2 = 2.003 · 10−20 m2/V2 optical density (see Eq. (9)), [−] radial coordinate with respect to switching beam axes (r ⊥ s), [m] beam radius (at 1/e2 of intensity), [m] propagation direction of switching pulse, [m] time, [s] temporal discretization, [s] transmission of the optical Kerr Gate, [−] pulse propagation velocity (group velocity) in CS2 : 1.809 · 108 m/s pulse energy, [J] propagation direction of imaging pulse, [m] radial coordinate with respect to imaging beam axes (y ⊥ x), [m] aperture width in y-direction, [m] coordinate (z ⊥ x, y), [m] angle between x- and s-axis, [◦ ]

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ε0 θ λ μ τl τp τo τgate Δφ

dielectric permittivity in vacuum: 8.854 · 10−12 F/m angle between Kerr cell axis and incident imaging pulse polarization, [◦ ] wavelength, [m] scattering coefficient, [1/cm] laser pulse duration (half width at 1/e of intensity), [s] laser pulse duration (full width at half maximum, fwhm, of intensity), [s] molecular relaxation time, carbon disulfide (from [3, 11, 19, 20]): 2 · 10−12 s full width of the gate opening time at half maximum, [s] phase shift experienced by imaging pulse, [rad]

Acknowledgments This work was performed as part of the Cluster of Excellence "Tailor-Made Fuels from Biomass", which is funded by the Excellence Initiative of the German federal and state governments to promote science and research at German universities. The authors also thank Mark Linne, Megan Paciaroni and Mattias Rahm for the fruitful discussions.

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