Open Access
Add to BibSonomy
Abstract
The ability to modify the lens focal length has an advantage of giving sharp images without moving the lens. This work presents for the first time the use of the thermal lens as a tunable imaging element of the microscope. It shows also that the thermal lens can modify the image of a selected area of the sample, leaving the rest part of the image unaffected. Thus, appropriate tuning of thermal lens can lead to a simultaneously sharp image of two objects lying in different object planes separated by a distance exceeding the depth of field of the imaging optics.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years different groups have attempted to build an optical lens with modifiable focal length. The most obvious idea was to imitate the human eye lens, whose focal length is changed by deformation of the lens shape by eye muscles. Such tunable lenses can be divided into three groups. The first is that of macroscopic size lenses, represented e.g. by the artificial accommodating intraocular lens [1] or the elastic polymer-based liquid lenses [2–5]. The second one is the group of microscopic size lenses based on elastic polymers [6] or electrostatic deformation of liquid droplets [7–9]. To the third group belong optical elements with modifiable distribution of refractive index of the optical material they are made of. Such elements belong to the gradient-index (GRIN) optics area, which is best known for the GRIN fiber and GRIN fiber collimator lens [10]. They are represented by the flame lens [11], tunable acoustic GRIN lens [12], electrically tunable liquid crystal lens [13] or the thermal lens [14]. The last one is especially well known among laser engineers, as its formation within lasing medium or at the surface of high power laser mirrors is one of many phenomena they try to avoid. On the other hand, in the last three decades thermal lensing has become an interesting spectroscopic tool [15] that has been even incorporated into the microscope [16,17]. Recently, it has been shown that thermal lensing may be used to actively compensate for deformation of high power laser beams [18].
Recently, Angelini et al. [19] have presented a liquid polymer photo-responsive tunable lens, that inserted into a microscope setup allowed a modification of the plane of focus of the microscope without movement of the sample. It is interesting to note that despite being widely studied for decades now, thermal lens has never been envisaged as such an imaging element of the microscope. Note that the term thermal lens microscopy [16,17] refers to the technique of measuring ultra-small absorption signals from a microscopic probe, not to thermal lens imaging ability. To the best of author knowledge, this article presents for the first time such an ability. The setup described herein allows a continuous focusing of the image acquired by the microscope without any mechanical displacement of any part of the microscope neither of the sample. The focusing range of up to 500 μm, presented in the paper, can be magnified by following setup modifications given in the article. A comparison of quality of the acquired image with/without active thermal lens is given. Thermal lens focal length tunability as well as information on its dynamics is reported. Finally, for the first time, the application of thermal lens in simultaneous imaging of objects lying in two different object planes is presented, a new technique that may be complementary to other microscopic imaging methods.
Thermal lens in the microscope
The thermal lens can be formed by illumination of an absorbing material with a heating laser beam. Absorption of this beam leads to heat deposition within the material. Consequently, a temperature gradient appears. According to the Lorentz-Lorenz formula [20], the refractive index of a material may depend on temperature through the temperature dependence of the material density or polarizability. As a consequence of laser heating a gradient of the refractive index, ∇n, appears within the material. It depends on the thermo-optical factor, ∂n/∂T, which is negative in liquids and polymers [21,22], while in solids it may be positive [23]. In terms of absolute values ∂n/∂T is clearly higher in liquids and polymers, because its magnitude is controlled mainly by density temperature dependence. In solids the change in density with temperature is counteracted by the change in polarizability [24]. The difference in ∂n/∂T for different states is by 2 orders of magnitude, therefore thermal lenses formed in liquids or polymers are of significantly higher optical power. Polymers are the best choice, as they do not exhibit heat convection and are much simpler to manipulate. Preparation of a liquid sample is much simpler, therefore, for the sake of demonstration of the technique, a liquid thermal lens has been used in this work. For continuous heating laser illumination, the focal length of thermal lens reads [25]:
where α is thermal lensing material extinction coefficient at excitation wavelength λe, L is the length of the material measured in the direction of the heating laser beam propagation, k is the thermal conductivity of the material, PHL and ωe are heating laser beam power and radius (measured at e−2), ϕF and are the thermal lensing material fluorescence quantum yield and fluorescence spectrum first spectral moment. Controlling PHL allows the tuning of the thermal lens focal power and this technique was used in this work.2. Methods
Thermal lens was incorporated into a brightfield home-made microscope setup in the way shown in Fig. 1. The microscope consisted of a Köhler type illuminator, followed by a Carl-Zeiss-Jena apochromatic objective (fobj = 11 mm, NA = 0.30, × 15, inf). The position of the sample was modified using a micro-positioning Z-stage. The microscope illumination and objective optical axis were aligned vertically. This allowed the horizontal placement of the cuvette containing the thermal lensing liquid. In this way, asymmetric distortion of the lens following from heat convection was of no concern. The thermal lens was formed within a glass cuvette of 18 × 21 × 5 mm in size filled with an ethanol solution of 5,10,15,20-Tetraphenyl-21H,23H-porphine (Sigma-Aldrich). The porphine solution extinction coefficient was determined from the absorption spectrum measured with a Jasco V-550 spectrometer at 405 nm, that is the heating laser wavelength. It was α = 247.5 m−1. The cuvette was placed on top of the objective nosepiece mounting thread (it was lying on the thread end). Directly above the cuvette an iris diaphragm (TL diaphragm) was placed, that acted as the aperture stop, whose opening diameter was set to the values given in Fig. 2 caption.
Fig. 1 Scheme of the microscope setup with the thermal lens (TL) used as tunable optical element of the imaging part.
Fig. 2 Images of positive USAF 1951 and Siemens Star resolution targets obtained at different relative vertical dz positions, different heating laser beam widths and TL diaphragm opening diameters. Label and frame color indicates TL diaphragm aperture diameter: d = 3 mm (red), d = 4 mm (blue), d = 11 mm (green). When fully opened (green) TL diaphragm aperture was wider than the microscope objective exit aperture. Heating laser beam radius ωe = 550 μm (a-j), ωe = 360 μm (k,l). Images (a), (e), (h) and (k) were obtained at dz = 0 and PHL = 0 without thermal lens active. On the right side of labels the dz and PHL values are given at which appropriate images were taken. Siemens Star concentric circles are of radii from 50 µm to 250 µm in 50 µm intervals. The scale bars represent 50 μm.
Next, a dichroic mirror was positioned, which reflected the imaging light in the direction of the camera, while it was letting pass the light of the heating laser beam. After the dichroic mirror a camera lens (Carl Zeiss Jena Biotar 1.5/75 mm) was used as the projective eyepiece and formed the image of the sample at the camera chip (Sumix SMX-M95M). The achieved optical magnification as deduced from the camera pixel size and USAF 1951 resolution test pattern bars sizes was found to be × 3.35, finally increased by the display (monitor) magnification. Maximal field size was 1.4mm in diameter. The USAF 1951 and Siemens Star resolution test targets, and the 50 μm grid pattern were printed on the same plate (Thorlabs, R1S1L1P).
A Pavillion Integ. diode UV laser (λe = 405 nm, 35 mW) was used as the source of heating beam. Laser exit was followed by a computer controlled shutter that was used to switch on/off the thermal lens when determining its formation/disappearance dynamics. Next, a round continuously variable metallic neutral density filter (Thorlabs) mounted in a motorized Standa rotation stage was used to control PHL. Prior to other measurements, PHL at the cuvette was measured as a function of the neutral density filter rotation angle and found to depend nonlinearly on this angle. In order to keep a constant step of the quantity that was the direct source of change in PHL, when determining thermal lens focal length dependence on PHL, the filter angle was modified which resulted in non-uniformly distributed values of laser power. Next, the laser beam was coupled into a multimode fiber (100 μm core, NA = 0.22) using an f = 20 mm quartz lens at an adjustable angle. Changes in the angle modified the beam profile at the fiber exit. Finally, at the fiber exit another f = 20 mm quartz lens was used to form the beam with desired width at the cuvette with thermal lensing porphine in ethanol solution. Using this method the heating laser beam profile of super-Gaussian shape and order equal 2.35 was selected. The beam profile was measured using the reflection of the heating laser beam from the dichroic mirror with another camera (Sumix SMX-150M) and a home-made beam profiling software.
The porphine in ethanol solution was chosen as it met several features expected of the thermal lensing material. It has a high absorption coefficient at the wavelength λ = 405 and its absorption spectrum is narrow ( = 413nm, FWHMabs = 12nm). Therefore, it does not absorb significantly the light used to image the sample in the microscope. Porphine dissolves very well in ethanol and – what is the most important – it has a low (< 0.1) fluorescence quantum yield [26]. Therefore, the absorbance of its solution can be selected in a wide range, its fluorescence does not contribute significantly to what is observed through the microscope and most of the energy absorbed from the heating laser beam by porphine is converted into heat.
Applications used to follow image sharpness and measure beam profile were written in NI LabView. Sharpness was evaluated using a derivative interpolation based metric by convoluting the acquired image with a Gaussian filter [27]. It was also always eye inspected. Thermal lens focal length was determined from the dependence of the sample position that gave a sharp image, on PHL. The imaging equation for two thick lenses was used in order to determine fTL [28]:
where s is the location of the focal point of the combined system, measured from the second principal point of the objective, while h is the distance between the second principal point of the thermal lens and the first principal point of the objective. Values of s were assumed to be the distance from the focal point to the objective entry surface (nearest surface to the sample) and were determined from dz values. Value of h was unknown but found to have minor influence on fTL, when checked in the range of 0 to 20 mm, which at maximum exceeded the distance between the objective center and the thermal lens cuvette exit surface (the one furthest from the objective). An arbitrary value of 10 mm was assumed. The curve fitted to fTL values was modeled by Eq. (1), assuming ϕF = 0. Values of k and ∂n/∂T for ethanol were taken from [21].3. Results
At first, operation of the thermal lens was checked by recording the image of the positive USAF 1951 and Siemens Star resolution targets at different dz positions, moving the targets using the Z-stage [Fig. 1]. The diameter of the heating laser beam and the TL diaphragm aperture were varied as well. Figure 2 presents representative images acquired with the condenser aperture small enough and camera exposure and gain kept relatively small in order to retain imperfections of the images obtained with the active thermal lens. When looking for a sharp image PHL was changed.
Siemens Star targets images were used to determine modulation transfer function (MTF) of the microscope optics in the way described in [29]. Similarly, as for USAF 1951 target, images of Siemens Star were taken at three d values of TL diaphragm aperture. Figure 3 presents the obtained results. MTF values do not decrease to 0 because of the method of determination of Siemens Star bars reference modulation pattern [29]. It relied on thresholding the recorded image of the Siemens Star, which led to erasure of any modulation at highest spatial frequencies, making evaluation of MTF impossible at these frequencies. Thermal lens introduces errors in the image, which are most important when its aperture is significantly smaller than the field stop of the microscope. Closing the aperture of the TL diaphragm [Fig. 2, Fig. 3] increases the image contrast at small spatial frequencies both when thermal lens is inactive and active. For higher frequencies the resolution decreases with thermal lens inactive (as expected), but increases with thermal lens active. Finally, the images obtained at the smallest TL diaphragm opening (3 mm) are not very different in quality at high spatial frequencies, as can be deduced from Fig. 3 (blue and pink lines) and Figs. 2(h) and 2(j).
Fig. 3 MTF of the microscope imaging optics as determined from the Siemens star resolution target images obtained without thermal lens active (dz = 0, PHL = 0, black, red and blue lines), and at a displacement of dz = 250 mm with thermal lens active (PHL = 11 mW, brown, green and pink lines). TL diaphragm diameters: 11 mm (black, brown), 4 mm (red, green), 3 mm (blue, pink). MTF for spatial frequencies corresponding to Siemens Star void rings approximated by linear dependencies imaged by dotted lines.
Next, the dependence of thermal lens focal length fTL on PHL was determined. To obtain it, the sample shift dz giving a sharp image was measured as a function of PHL, relative to dz found at PHL = 0. Then, fTL was determined from Eq. (2). Figure 4 presents the dz(PHL) and fTL(1/ PHL) dependencies. The curve fitted to fTL values [Fig. 4(b)], according to Eq. (1), confirmed f(1/ PHL) dependence. However, the heating laser beam radius, set as fit parameter, was found to be ωeFit = 1400 μm, 2.5 × greater than the measured ωe (550 μm). Measurements made at 4 × higher concentration of porphine led to similar differences.
Fig. 4 Dependence of: (a) dz position of the USAF 1951 pattern that gave pattern sharp image at different heating laser power PHL, as measured relative to the position at PHL = 0; (b) thermal lens focal length f(PHL) dependence determined from (a). TL diaphragm opening diameter was set to 4 mm and heating laser beam radius at thermal lens cuvette was found ωe = 550 μm.
To detect possible saturation effects, the thermal lensing sample absorption was measured at each PHL in the microscopic setup, also with the sample cuvette empty. No sign of saturation was detected. The model used to derive Eq. (1) assumes that the thermal lensing sample is thin and no convection takes places inside the sample during heating, and that the thermal lens is formed using a laser beam of Gaussian profile. All these assumptions were not fulfilled for the thermal lens used in this work. Convection is the most probable source of discrepancy between what follows from Eq. (1) and the measured ωe value. In the case of cw vertically illuminated thermal lens, as in this work, convection has to increase the lens diameter, diminishing simultaneously its effective length (focal as well). No analytical formulae for thermal lens focal length, taking into account such an effect is known by the author. It may be solved numerically, in a way similar to that taken in [30]. However, such studies were out of the scope of this work. Errors in fTL values [Fig. 4(b)] were computed by error propagation of dz error.
Usually, the thermal lens dynamics is determined by measuring the change in intensity of a probe laser beam that travels through the thermal lens, after heating laser switched-on/off. As a result of lens divergence this intensity drops at the center of the probe beam and can be accurately monitored using a photodiode and oscilloscope [31]. Thermal lens formation can take a few ms for very small lenses [32], up to hundreds of ms or even seconds. In order to use the same microscope setup the thermal lens formation and disappearance dynamics was determined from the change in sharpness of the Siemens Star target, in response to the heating laser switching on/off [Fig. 5]. Sharpness as evaluated here does not have to be linearly dependent on fTL. Therefore, no modeling of the formation and disappearance of the thermal lens was made. It is worth noting that there are the formulas that allow evaluation of fTL(t) [25,33]. They show that the thermal lens dynamics is governed by the thermal time constant τc = ωe2ρcp/(4k), where ρ is the thermal lensing medium density and cp is its specific heat. For ωe = 550 μm and the thermal lensing material used in this work, τc = 433 ms, for ωe = 360 μm τc = 185 ms. A wide thermal lens, of a size similar to the objective exit aperture, ωe = 3 mm would be formed slowly with τc = 13 s.
Fig. 5 (a) Time dependence of the sharpness factor of the Siemens Star target image acquired after heating laser switched-on (t = 1.5 s) and switched-off (t = 21.5 s). Panels (b) and (c) present selected time ranges of the graph (a). Measurement taken at PHL = 11 mW, ωe = 550 μm, dz = 250 μm.
Finally, the thermal lens was applied for visualization of two objects, lying at two distinct planes, separated by a z distance exceeding the microscope objective depth-of-field. Figure 6 presents an image of a 50 μm grid pattern lying over a microscopic sample with a Cucurbita Stem cross section. The reader is encouraged to take a look at Visualization 1, which presents the effect of modification of the position and focal power of the thermal lens on the image acquired.
Fig. 6 Images of a 50 μm grid pattern lying over a microscopic sample with a Cucurbita Stem cross section. Two microscope cover slips separated the samples by 390 μm, as deduced from dz position shifts of the samples required to obtain a sharp image of the grid pattern (a) and Cucurbita Stem cross section (d). Image (b) shows both samples without thermal lens active with the microscope objective focused at the intermediate plane between planes shown in images (a) and (d) (dz = 195 μm). Image (c) shows both samples at dz position the same as in (a), with thermal lens formed in the area indicated by the circle, PHL = 5.5 mW, ωe = 360 μm. Microscope aperture stop was in this case significantly wider than the thermal lens aperture. The area of the Cucurbita Stem imaged by the thermal lens is sharp, as well as the grid pattern in other parts of the view field. The scale bars represent 100 μm.
4. Discussion
It is known that the thermal lens optical aberrations are strongly connected to the heating laser beam profile [14]. Up to now, the top-hat profile has been recognized as the most appropriate one. The profile of heating laser obtained in this work was far from being of top-hat shape, it was not even perfectly symmetric. Nevertheless, it is encouraging to see that this imperfection did not affect strongly the image quality obtained with the thermal lens active. It is evidenced by inspection of Figs. 2(h) and 2(j) images and modulation transfer functions (MTF) obtained from Siemens Star target images analysis. Figure 2 shows that it is the numerical aperture (NA) of the thermal lens that limits its resolution, as expected. Increasing thermal lens NA, while keeping constant the lens focal length, requires heating laser of higher power, not available during this work. It follows from the fact that the lens aperture is determined by the heating laser beam width, ωe. As can be deduced from Eq. (1) one has to increase PHL when a bigger ωe is needed. Therefore, the microscope resolution was subsequently decreased, by closing the TL diaphragm. This allowed to establish that at sufficiently small TL diaphragm opening diameter, the images taken with thermal lens active [Figs. 2(d) and 2(j)] are of quality close to those taken with thermal lens switched-off [Figs. 2(a) and 2(h)]. The lack of laser of high enough power forced a decrease in the heating laser beam diameter, in order to obtain smaller thermal lens focal length absolute value. This inevitably led to a decrease in resolution as shown in Figs. 2(k) and 2(l). On the other hand, an increase in the laser beam width slows down the dynamics of thermal lens formation and disappearance. Thus, the use of a thermal lens in a microscope setup requires a compromise between lens resolution and focal length tuning speed. The lens tunability is governed by focal length inverse PHL dependence [Eq. (1), Fig. 4]. It means active accommodation may require different times, depending on the PHL range currently used. Figure 5 shows that at the setup parameters used in this work, thermal lens formation and disappearance are relatively slow. However, one should note that in practical circumstances the user will probably not change the lens fTL as abruptly. Equation (1) shows that if one uses a material with higher k in order to speed up thermal lens formation and disappearance dynamics, the lens focal length will decrease making it less useful. Therefore, when used in high NA mode the thermal lens should be treated as an accurate, motionless and stable but a slow focusing tool. Maximum PHL determines the range of fTL changes in the thermal lens. For PHL and ωe, as used in Fig. 4, fTL changes from −20m to −0.5m. Increasing PHL will lead to shorter fTL, but one has also to consider saturation effects that will inevitably appear at a too high PHL. Thus, when designing a setup of particular range of fTL changes one should select carefully the absorption of the thermal lensing material, thus the concentration of the absorbing medium. This medium should in principle absorb only the heating laser light. Therefore, it should have narrow band absorption and this property was fulfilled by the dye used in this work. But, for best performance the heating laser light absorption should take place in the infrared (IR) and an IR laser should then be applied. This will allow full color image acquisition of samples, making thermal lens much more useful.
The most intriguing feature of the thermal lens, as used in this work, is the possibility to track an object in a plane different from the principal focal plane of the microscope objective as shown in Fig. 6. Both planes may be separated by a distance exceeding the depth-of-field of the objective. It does not allow simultaneous observations of different z slices of the sample at the same xy coordinates, as does e.g. the technique described in [34]. However, thermal lens allows a simultaneous and continuous observation of different objects without need for post-processing image analysis, required in [34]. Additionally, these objects may move in all directions and may even be multiple, as many thermal lenses can be formed using different heating laser beams. But note that all these objects will lie in planes more distant from the microscope objective than its own focal plane. These object images will be magnified differently, but this difference will not be very significant (compare outer ring diameters in Siemens Star images in Fig. 2(h) and 2(j)). In principle, one can envisage using the spatial light modulator (SLM) or the continuous deformable mirrors (DM) in order to achieve such functionality. SLMs have a limited phase delay, which can be applied to light, therefore a diffractive pattern such as the Fresnel zone plate has to be displayed by the instrument in order to focus light. However, the Fresnel zone plate has a diameter proportional to the square root of its focal length [35]. Therefore, in case of binary amplitude/phase Fresnel zone plate it is not possible to focus light on a particular plane without changing the lens diameter. Thus, such pattern does not provide the same functionality as the thermal lens does. One can consider using a phase only SLM, displaying a continuous Fresnel zone plate pattern [36], instead of the thermal lens. However, a direct comparison of both techniques, in terms of their imaging capabilities, is required before deciding whether the SLM may replace the thermal lens. DM can be addressed and configured much faster, than thermal lens focal length can be changed [37]. Additionally, it does not suffer of chromatic aberrations. However, DM has a limited number of actuators. This means it is not possible to change smoothly the position of the smallest curved mirror that can be formed by a single DM actuator. Therefore it is not possible to continuously track a moving object as can be done using the thermal lens formed by a laser beam, whose position in the thermal lensing material is smoothly changed.
5. Conclusions
In conclusion, this work shows that the thermal lens may be used as an active optical element of the microscope. The focal length of the thermal lens may be changed in a relatively wide range, leading to microscopic images of acceptable quality, which can be ameliorated by better heating laser beam profile formation and more suitable thermal lensing material selection. When looking for a sharp image using such lens, there is no need for mechanical displacement of any part of the microscope.
The most important achievement of this work is the finding of a new visualization technique whose operation result is shown in Fig. 6. Using the thermal lens (and other laser formed lenses as well) it is possible to obtain a sharp image of an object lying in a plane different from the one at which is focused the rest of the optical setup, whose part the thermal lens is. In this work the optical setup was the microscope. In principle it may be a camera lens as well.
References and links
1. “Accommodating Intraocular Lens (Aiol), and Aiol Assemblies Including Same,” United States patent 20070244561 A1, NuLens.
2. “Liquid lens system,” patent WO 2009021344 A1 and patents cited in, Optotune.
3. H. Yu, G. Zhou, H. M. Leung, and F. S. Chau, “Tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation,” Opt. Express 18(10), 9945–9954 (2010). [CrossRef] [PubMed]
4. M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14(12), 1665–1673 (2004). [CrossRef]
5. D.-Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y.-H. Lo, “Fluidic adaptive lens with high focal length tenability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003). [CrossRef]
6. J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable-focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14(5), 675–680 (2004). [CrossRef]
7. S. Kwon and L. P. Lee, ”Focal length control by microfabricated planar electrodes-based liquid lens (μPELL),” in Proceedings of 11th International Conference on Solid State Sensors and Actuators Transducers (2001), pp. 1348–1351. [CrossRef]
8. B. Berge, “Liquid lens technology: principle of electrowetting based lenses and applications to imaging,” in Proceedings of 18th IEEE International Conference on Micro Electro Mechanical Systems (IEEE, 2005), pp. 227–230. [CrossRef]
9. C. C. Cheng, C. A. Chang, and J. A. Yeh, “Variable focus dielectric liquid droplet lens,” Opt. Express 14(9), 4101–4106 (2006). [CrossRef] [PubMed]
10. D. T. Moore, “Gradient Index Optics,” in Handbook of Optics Vol. I, 3rd Edition (McGraw Hill, 2010).
11. M. M. Michaelis, C. Mafusire, J.-H. Grobler, and A. Forbes, “Focusing light with a flame lens,” Nat. Commun. 4, 1869 (2013). [CrossRef] [PubMed]
12. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33(18), 2146–2148 (2008). [CrossRef] [PubMed]
13. H.-C. Lin and Y.-H. Lin, “An electrically tunable-focusing liquid crystal lens with a low voltage and simple electrodes,” Opt. Express 20(3), 2045–2052 (2012). [CrossRef] [PubMed]
14. M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, “Adaptive beam shaping by controlled thermal lensing in optical elements,” Appl. Opt. 46(12), 2153–2165 (2007). [CrossRef] [PubMed]
15. M. A. Proskurnin, D. S. Volkov, T. A. Gorkova, S. N. Bendrysheva, A. P. Smirnova, and D. A. Nedosekin, “Advances in thermal lens spectrometry,” J. Anal. Chem. 70(3), 249–276 (2015). [CrossRef]
16. K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, and T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000). [CrossRef]
17. J. Moreau and V. Loriette, “Confocal thermal-lens microscope,” Opt. Lett. 29(13), 1488–1490 (2004). [CrossRef] [PubMed]
18. Z. Liu, P. Fulda, M. A. Arain, L. Williams, G. Mueller, D. B. Tanner, and D. H. Reitze, “Feedback control of optical beam spatial profiles using thermal lensing,” Appl. Opt. 52(26), 6452–6457 (2013). [CrossRef] [PubMed]
19. A. Angelini, F. Pirani, F. Frascella, S. Ricciardi, and E. Descrovi, “Light-driven liquid microlens,” Proc. SPIE 10106, 1010610 (2017).
20. M. Born and E. Wolf, Principles of Optics, Ed. 7 (Cambridge University, 1999), Chap. 2.3.
21. Y. Marcus, The Properties of Solvents, Wiley Series in Solution Chemistry Vol. 4 (Wiley, 1998).
22. S. N. Kasarova, N. G. Sultanova, and I. D. Nikolov, “Temperature dependence of refractive characteristics of optical plastics,” J. Phys. Conf. Ser. 253, 012028 (2010). [CrossRef]
23. M. J. Weber, Handbook of Optical Materials (CRC, 2003).
24. G. Ghosh, “Handbook of Thermo-Optic Coefficients of Optical Materials with Applications,” in Handbook of Optical Constants of Solids Vol. 5, E.D. Palik, (Academic, 1998).
25. J. R. Whinnery, “Laser measurement of optical absorption in liquids,” Acc. Chem. Res. 7(7), 225–231 (1974). [CrossRef]
26. R. T. Kuznetsova, N. S. Savenkova, G. V. Mayer, P. A. Shatunov, and A. S. Semeikin, “Physical-chemical properties of tetraphenylporphyrin, its octasubstituents, and complexes with metals in the ground and excited states,” Atmos. Oceanic Opt. 17(2–3), 149–155 (2004).
27. M. Rudnaya and R. Ochshorn, “Sharpness Functions for Computational Aesthetics and Image Sublimation,” Int. J. Comput. Sci. 38(4), 359–367 (2011).
28. R. B. Johnson, “Two-lens systems,” in Handbook of Optics Vol. I, 3rd Edition, (McGraw Hill, 2010).
29. J. Otón, C. O. S. Sorzano, R. Marabini, E. Pereiro, and J. M. Carazo, “Measurement of the modulation transfer function of an X-ray microscope based on multiple Fourier orders analysis of a Siemens star,” Opt. Express 23(8), 9567–9572 (2015). [CrossRef] [PubMed]
30. H. D. Doan, Y. Akamine, and K. Fushinobu, “Fluidic lens by using thermal lens effect,” Int. J. Heat Mass Transfer 55(23–24), 7104–7108 (2012). [CrossRef]
31. J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. 165(2–3), 385–396 (1992). [CrossRef]
32. M. L. Baesso, J. Shen, and R. D. Snook, “Modemismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75(8), 3732–3737 (1994). [CrossRef]
33. J. Skupiński, J. Buchert, S. Kielich, J. R. Lalanne, and B. Pouligny, “Thermal lens effect applied in thermal diffusion determinations for molecular liquids,” Acta Phys. Pol. A 67, 719–726 (1985).
34. S. Liu and H. Hua, “Extended depth-of-field microscopic imaging with a variable focus microscope objective,” Opt. Express 19(1), 353–362 (2011). [CrossRef] [PubMed]
35. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (John Wiley & Sons, 2007), Chap. 4.1.
36. E. C. Tam, S. Zhou, and M. R. Feldman, “Spatial-light-modulator-based electro-optical imaging system,” Appl. Opt. 31(5), 578–580 (1992). [CrossRef] [PubMed]
37. W. J. Shain, N. A. Vickers, B. B. Goldberg, T. Bifano, and J. Mertz, “Extended depth-of-field microscopy with a high-speed deformable mirror,” Opt. Lett. 42(5), 995–998 (2017). [CrossRef] [PubMed]
