Table of Contents
PSF and SR definitions in the photomodulated image
Measurement Result and Analysis
This article explains a far-field, label-free super resolution (SR) microscopy approach which relies on inducing a spatial distribution of physical properties - temperature or carrier concentration - by an ultrashort laser pulse within the photo-excited diffraction limited spot. By monitoring the nonlinear response of any property of the sample, which depends on this spatial distribution - for example the temperature - label-free spatial information with higher resolution as given by the diffraction limit may be obtained.
PSF and SR definitions in the photomodulated image
The theory behind the nonlinear photo-modulated reflectance (NPMR), an example of label-free super resolution microscopy, is discussed in Refs. [1, 2]. Although NPMR is the result of numerous physical effects, focus will be on the thermal excitation and the probing of thermoreflectance (TR). In TR, one utilizes the changes of reflectance upon heating to measure thermal properties of materials or to map heating using linear models. Measuring nonlinear components of TR in response to photo-excitation enables the significant reduction of the effective point spread function (PSF), resulting in an enhanced resolution.
The image resolution in case of linear TR is determined by the pump and probe intensity profiles, the pump probe time delay, and the scanned object. In this investigation, a temperature profile identical to the laser Gaussian intensity distribution with standard deviation σpump, which is valid for short pump-probe delays of about 0–3 ps was considered. The probe beam has a Gaussian shape with standard deviation σprobe.
Consequently, the linear TR image P(x,y) comprises the product of the pump and probe images, convolved with the object function O(x,y):
P(x,y) = (PSFpump •PSFprobe)⊗O(x,y) = PSFTR ⊗O(x,y)
= Ipumpe− r2 /2σpump Iprobee− r2 2σprobe (t = 0)⊗O(x,y).
The effective point spread function in the linear TR, PSFTR, can be gained by deconvolution of the image with the object, resulting in a Gaussian function with a standard deviation of
σTR =√ (σ2pumpσ2probe/ σ2pump + σ2probe).
For a pump beam with half the wavelength of the probe, the resolution enhancement over an electrically heated sample with the same diffraction-limited probe beam is √5. In the case of identical wavelengths for pump and probe beams, this enhancement is only √2. Incorporating pump-induced nonlinearities improves the resolution beyond the linear case.
Figure 1. Simulated profiles of the effective PSF on the on the lateral (r) axis calculated from the PSF and the n-th order of the pump intensity distribution. The blue curve represents a probe reflection scan, while the other curves correspond to the n-th order of TR.
Figure 2. Optical setup comprising dichroic mirrors (DM), an acousto-optic modulator (AOM), a beam splitter (BS), and a photodiode.
For a given suspension between pump and probe, the relative alteration in reflectivity as a function of temperature T, can be characterized as a Taylor series:
∆R R (α,T) = a1(α)T + a2(α)T2 + a3(α)T3 +•••
where α is a material dependent parameter. If the pump excitation is a pure sine wave with modulation frequency ω, the temperature is also a harmonic function, T(α) = Ib0(α)eiωt, where the parameter b0 is dependent on the material and relates the incoming intensity I to the temperature. The time-dependent thermoreflectance ∆R/R is then given by
∆R R ≈a1Ieiωt + a2I2ei2ωt + a3I3ei3ωt +•••
where the dependences on α were omitted for clarity’s sake. By distinguishing the modulation at different harmonics of ω, the non-linear response is measured. The nonlinear intensity profile measured at 2ω, 3ω,… is a Gaussian to the power of n=2, 3,…., which is finer than the first-order Gaussian as shown in Figure 1. Thus, a higher resolution is expected.
In order to measure the nonlinear response of the physical system, it is compulsory to excite the system with pure harmonic light intensity without distortions. An acousto-optic modulator(AOM), which intrinsically produces distorted light modulation, was used in combination with the UHFLI Lock in Amplifier and the UHF-AWG Arbitrary Waveform Generator to yield a pure sinusoidal excitation.
The optical apparatus is shown in Figure 2. An 800 nm beam (probe) with 100 fs pulse duration at the source is frequency-doubled to 400 nm (pump). The beams are parted by a dichroic mirror. A variable delay line is used to tune the timing of the probe relative to the probe beam and a successive dichroic filter combines the two beams into a reflection microscope.
Figure 3. LabOne AWG Sequencer program used for the experiment.
The pump beam at 400 nm is modulated at 54 kHz by means of an AOM together with the UHF-AWG as shown in Figure 4. To please the drive voltage requirements of the AOM RF driver, AWG signal can be created on one of the Auxiliary Outputs, thus providing a larger signal amplitude than the Signal Output of the UHFLI. The AWG output signal for the AOM is tailored to give a pure sinusoidal optical excitation. The probe reflectance is taken at different harmonics of the reference frequency using a photo diode and a UHFLI lock-in amplifier. To phase-lock the drive signal with the lock-in detection, a sinusoidal signal on Auxiliary Output 1 was created and fed back into Ref/Trigger Input 1 to be utilized as a lock-in reference signal.
The code block in Fig. 3 illustrated the LabOne AWG Sequencer program employed in this experiment. The customized wave form aux_ch2 used to generate the modulation signal is loaded from an external file unlike the sinusoidal wave form aux_ch1 for the reference signal which is created directly in the program. The two waveforms aux_ch1 and aux_ch2 are then played back to back in an infinite loop. The frequency of the generated signals is then defined by the AWG sampling rate when using the Auxiliary Outputs, 14.0625 MHz, divided by the number of samples in the wave form, 256.
Measurement Result and Analysis
Measuring higher harmonics of the TR relies on having a purely sinusoidal pump intensity modulation. Because the AOM has a nonlinear transfer function, its input signal should be distorted in a controlled manner in order to generate a pure harmonic output. Thanks to the multiple demodulators of the UHFLI, it is possible to measure the fundamental and higher harmonics of the modulated light intensity.
These results are fed to an iterative algorithm developed to update the AWG signal applied to the AOM to reduce the nonlinear components of the pump laser modulation. As an alternative to the AWG, the UHF-MF Multi-frequency option offers the functionality to superpose up to eight harmonics with individual amplitudes and phases on the Signal Output to fine-tune the AOM drive signal.
Figure 4. Electrical setup used to generate the pump beam modulation and to measure the photodiode signal. The AWG output on Auxiliary Output 1 is connected to the AOM driver. The photodiode signal is measured with the UHFLI. The Ref/Trigger connectors are used to phase-lock the UHF-AWG with the lock-in amplifier.
Figure 5. Pump signal’s Fourier transform measured with the Oscillsocope of LabOne user interface. The plot shows a prominent peak at the principal modulation frequency 54 kHz, while the 2nd, 3rd, 4th,... harmonics are about 80 dB below the amplitude of the main peak.
The Fourier transform of the pump signal is shown in Figure 5, displaying a prominent main peak at 54 kHz while peaks at higher harmonics are at least four orders of magnitude lower, thus proving the need for pure sinusoidal excitation. The SR scan of gold double lines on ITO nanostructures is shown in Figure6(c-e). Fitting a two-Gaussian model to the signal of 2nd harmony from the 4th pair of gold double lines (160 nm gap), yields a full width at half maximum (FWHM) of 227.5 ± 6.1 nm and 209.2 ± 5.6 nm for first and second peak, respectively, and a gap distance of 178 ± 2 nm. A similar fit for the 2nd harmony signal yields a FWHM of 142.9 ± 16 nm and 151.1 ±16.5 nm for the first and second peak, respectively, and a gap distance of 180 ± 2 nm.
The calculated gap matches closely with the measured gap size of 161 nm from the HR-SEM image in Figure 6(b). Furthermore, the narrowing of the FWHM by a factor of 1.5 parallels with the expected theoretical narrowing of the PSF by a factor of 1.34. The multiple demodulators of the UHFLI enable measurement of the thermoreflectance response at multiple harmonics concurrently which ensures that all signals are acquired under the exact same experimental conditions.
Figure 6. Super-resolution line imaging of gold on sapphire nanostructures. The sample consists of gold double lines, 125 nm wide, with decreasing gaps of 370, 270, 160, 160, and 120 nm, respectively. (a) High-resolution scanning electron microscope (HR-SEM) image of the sample. (b) HR-SEM zoom on one of the 160 nm gap double lines. (c-e) Line scan with a 0.95 NA objective using the 1st (c), 2nd (d), and 3rd (e) harmonic of the modulation.
This option also simplifies the experimental setup, as the alternative would be to use multiple lock-in amplifiers or to extend the data acquisition time in order measure the harmonics sequentially. Merging the drive and measurement in a single instrument helps reducing the risk for electrical cross talk and ground loops between different apparatus. This is of importance when measuring the nonlinear response signal, which is small and can be easily lost in electronic noise.
The process of super-resolution optical microscopy in a label-free sample using photomodulated reflectivity measured with the UHFLI has been described here. The multi-purpose digital nature of the UHFLI simplifies the experimental method by providing an all-in-one hub for the required A/D signal generation and detection. The ability for multi-harmonics demodulation and FFT readout is crucial for the generation and verification of a pure harmonic modulation.
The concurrent measurement of several harmonics saves measurement time and eradicates the need for multiple lock-in amplifiers. The resolution can be further enhanced by recording higher-order nonlinearities. The practical limit of attainable resolution is governed by lower power and signal-to-noise ratio in high harmonic response. Increasing the laser power to achieve higher nonlinearity is bracketed by the sample damage threshold.
Zurich Instruments would like to thank Dror Hershkovitz, Omer Tzang, Haim Suchowski, and Ori Cheshnovsky from Tel Aviv University for their contributions.
 Omer Tzang and Ori Cheshnovsky. Far-field super-resolution microscopy based on the nonlinear response of photothermal excitation. Proc. SPIE 9361, Ultrafast Phenomena and Nanophotonics XIX, page93610T, March 14,2015.
 Omer Tzang, Alexander Pevzner, Robert E. Marvel, Richard F. Haglund, and Ori Cheshnovsky. Super resolution in label-free photomodulated reflectivity. NanoLetters,15(2):1362–1367,2015.
This information has been sourced, reviewed and adapted from materials provided by Zurich Instruments.
For more information on this source, please visit Zurich Instruments.