Super-resolution imaging of photonic crystals using the dual-space microscopy technique

Abstract

We present an experimental implementation of the recently proposed dual-space microscopy (DSM), an optical microscopy technique based on simultaneous observation of an object in the position and momentum spaces, using computer-controlled hemispherical digital condensers. We demonstrate that DSM is capable of resolving structures below the Rayleigh resolution limit.

Toward Phase-Recovery Optical Nanoscopes

“…When NA c > NA o and λ/(NA o +NA c ) > λ/(2n), where (n) is the refractive index of the medium surrounding the sample, phase-recovery imaging techniques like FPM and DSM can be used to obtain a numerically-reconstructed high-resolution image with a resolution ~λ/(NA o +NA c ) < λ/(2NA o ) [23,24,27,28]. 22 The details o be discussed that it is fu developed a illuminated direction at a a low-resolu directly reco direction, re are then num algorithm [2 with a large the intensity field at the are numeric extended to simultaneou [31][32][33].…”

“…This is in contrast to single illumination-direction DSM, where the amplitude of the calculated FP-OD (a m,j,q (r)) is instead substituted by the square root of the intensity of the corresponding experimental (or simulated) low-resolution FP image [27,28]. The incoherent superposition condition, which requires that the sum of all modified intensities (I modFP, j,q ) contributing to the formation of the multiplexed low-resolution FP image number j should be equal to I FP,j .…”

“…Again, this is in contrast to single illumination-direction DSM, where the amplitude of the calculated RP-OD (a m,j,q (r)) is instead substituted by the square root of the intensity of the corresponding experimental (or simulated) low-resolution RP image [27,28]. Eq.…”

“…We conducted IDM-DSM simulations setting p(r)=0 and a(r) equal to the square root of the intensity corresponding to the first multiplexed low-resolution RP image used in the algorithm as the initial approximation of the RP-OD. We assumed a set of 64 illumination directions, each direction corresponding to an LED in a previously reported hemispherical digital condenser [27,28,33] Fig. 3 shows simulation results corresponding to a photonic crystal with rectangular symmetry and two different periods p x = 800 nm and p y = 340 nm, which were obtained using the IDM-DSM phase recovery algorithm described in Fig.…”

“…This is a second limitation of any image formed directly on a camera that is only sensitive to the intensity of the light [1,2,12]. Numerous optical microscopy techniques have been developed to overcome this second limitation of common optical microscopes [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]; however, none of the existing optical nanoscopy techniques permits imaging of the phase distribution of the electric field at the sample's plane. In this work we present a feasible route for the realization of the first optical nanoscope capable of imaging both the intensity and phase distributions of the electric field at the sample's plane.…”