J. Eur. Opt. Society-Rapid Publ. 21, 7( 2025) 61 d max ¼ 1
2k 0
:
This formulation is valid for 1st order linear Raman scattering. However, if the order of the scattering is higher, the maximum k s becomes proportional to the order of the scattering e. g. k s = 2k 0 for 2nd order non-linearity processes and k s = 3k 0 for 3rd order non-linearity processes leading to spatial resolution of 1 / 3k 0 and 1 / 4k 0 respectively. Unlike fluorescence signals, Raman signals are significantly narrower. Therefore, the method requires a narrow band filter and a spectrometer to achieve the chemical specificity.
The application of the CARS process to microscopy provides chemical information about a sample without labelling agents. The contrast in CARS microscopy arises from the signal enhancement when the frequency difference between the pump field x pump and the stokes field x Stokes is tuned to a Raman-active vibrational band [ 37, 38 ]. Unlike fluorescence imaging, CARS measurements are not background free. The non-resonant background from any objects of interest and the surrounding solvent limits the image contrast and spectral selectivity [ 37 ]. Several methods and strategies have been suggested for suppressing or separating the non-resonant background, including using a near-IR beam, polarization-resolved CARS, epi-detection CARS, and heterodyne CARS [ 39 – 41 ]. Also, the signal of the CARS process relies on the satisfaction of a phasematching condition between wave vectors of the excitation and emission fields( k CARS = 2 k pump � k Stokes, where k CARS, k pump, andk Stokes are the CARS signal( anti-Stokes), the pump and the Stokes wave vector, respectively) [ 42 ]. Additionally, the lateral resolution of CARS microscopy is diffraction-limited which depends directly on the CARSsignal wavelength k CARS, and inversely on the numerical aperture of the detection system NA det [ 43 ]. Therefore, adding super-resolution capability to CARS microscopy as a label-free super-resolution technique is a challenge.
To address this issue, Park et al. and Hajek et al. proposed a theoretical scheme based on SIM to improve the resolution of CARS microscopy. Park et al. demonstrated that the coherent image formation with the non-linear structured excitation framework has a potential to enhance resolution 2.7 times better than the conventional wide-field CARS system [ 43 ]. Hajek et al. theoretically showed that adding the structured illumination to the wide-field CARS configuration as a standing wave for the pump beam can improve the lateral resolution three-fold [ 44 ]. In summary, SIM based on the coherent process, such as CARS, requires the measurement of a coherent transfer function( CFT). Therefore, a precise mathematical framework requires to extract and reconstruct the super-resolution contents into an image with an enhanced resolution. As a result, in practice, extracting the high spatial frequency components of the object due to inherent coherent process of CARS is a complex and process.
3.1.3 Super-resolution SIM by photon statistics evaluation
A subset of super-resolution approaches that do not require non-linearity rely on assessing high-order correlations
( or fluctuation) in observed photon statistics to assure super-resolution when using non-Poissonian photon emitters. The sub-diffraction resolution improvement scales with the square root of j, where j is the highest order central moments of the photocounts distribution. Statistical quantum correlation analysis has been used in wide-field and confocal settings [ 45, 46 ] with single-photon detectors, as well as the super-Poissonian classical counterpart with linear detectors [ 47 – 49 ]. The latter method is known as Super-resolution Optical Fluctuation Microscopy( SOFI).
The integration of those photon statistics superresolution methods with SIM has been demonstrated theoretically to provide a much more favourable( linear) scaling, with the correlation order j [ 50 ]. The principle has been applied experimentally both for wide field SOFI [ 51 ] and for quantum image scanning microscopy [ 52 ].
The results of this work are detailed in another publication to be submitted as an extra publication. However, a preprint can be found on arXiv [ 53 ].
3.2 Deterministic functional pump / probe techniques
Most deterministic functional pump / probe SRM techniques, which can be summarised as RESOLFT-like methods [ 54 ], are based on four building blocks:
1. A switchable detection channel which is usually realised by state population control or modification( in e. g. [ 55 ] denoted as“ switching states on and off”). 2. A detection channel or contrast mechanism, respectively, which usually is the fluorescence emitted by the fluorescence markers.
3. To achieve real superresolution a non-linearity( such as saturation) of the detection signal and the lightmolecule interaction is obligatory.
4. Finally, a spatial field shaping( e. g. to provide a donut beam profile) usually of the probe beam is required to enable in combination with the non-linearity a tailoring of the PSF of the microscope imaging.
To achieve label-free SRM schemes many different detection channels as alternatives to fluorescence of marker molecules have been proposed, theoretically analysed and in many cases also experimentally demonstrated including autofluorescence,( transient) absorption, Raman, photothermal detection or photo-modulated reflectivity( cf. [ 13 ] and references therein).
As already described in Section 3.1.3, exploitable nonlinearities besides saturation, different second order( e. g. SHG or two-photon emission fluorescence 2-PEF) and third order( such as third harmonic generation SHG or CARS) non-linearities have been proposed and demonstrated [ 32 ].
Switchable detection channels in a STED-like microscopy scheme can be realised in many four-level systems with suitable state lifetimes and transition rates, respectively. Autofluorescence in the material under test would be of course an easy and self-evident option. However, in most cases the reachable contrast and resolution might be limited and an SRM method based on autofluorescence would require quite flexible pump and probe wavelengths