Unlabeled Far-Field Deeply Subwavelength Topological Microscopy (DSTM)

Abstract

A nonintrusive far-field optical microscopy resolving structures at the nanometer scale would revolutionize biomedicine and nanotechnology but is not yet available. Here, a new type of microscopy is introduced, which reveals the fine structure of an object through its far-field scattering pattern under illumination with light containing deeply subwavelength singularity features. The object is reconstructed by a neural network trained on a large number of scattering events. In numerical experiments on imaging of a dimer, resolving powers better than λ/200, i.e., two orders of magnitude beyond the conventional "diffraction limit" of λ/2, are demonstrated. It is shown that imaging is tolerant to noise and is achievable with low dynamic range light intensity detectors. Proof-of-principle experimental confirmation of DSTM is provided with a training set of small size, yet sufficient to achieve resolution five-fold better than the diffraction limit. In principle, deep learning reconstruction can be extended to objects of random shape and shall be particularly efficient in microscopy of a priori known shapes, such as those found in routine tasks of machine vision, smart manufacturing, and particle counting for life sciences applications.

Keywords: machine learning; microscopy; superoscillations; superresolution; unlabeled.

Figure 1

Deeply subwavelength topological microscopy (DSTM) schematic. The imaged object (a dimer A–B–C) is illuminated with a superoscillatory light field. The intensity profile of the diffraction pattern resulting from scattering of the superoscillatory light field on the imaged object is detected by the detector array. A number of different diffraction patterns are recorded when the illuminating field is scanned against the object. Left and right panels show maps of intensity and phase profiles of the illuminating field and indicate the presence of hotspots and phase singularities, where m indicates the winding number of the singularity.

Figure 2

Deeply subwavelength topological microscopy of a dimer. a) The dimer consists of two elements with different sizes A and C separated by a gap (edge‐to‐edge) B. It is positioned in the object plane at distance D from the x = 0 points of the object plane (see Figure 1). Two different regimes are presented, where the dimer position is either b,c) known (fixed at D = 0), or d–f) unknown. b,c) The retrieved values of B and A presented against their actual values, when D is known. Solid blue and red lines correspond to the median of the true values under superoscillatory (blue squares) and plane wave illumination (red circles), while the red and blue colored bands indicate the corresponding interquartile (IQR) ranges (see also the Supporting Information). In the case of unknown position, panels (d)–(f) show the retrieved values of D, B, and A presented against their actual values. Retrieved values for size C are similar to size A.

Figure 3

Resolution of the deeply subwavelength topological microscopy. IQRs of measured values of the dimer dimensions, a,d) gap, B, b,e) element size, A, and c) position, D, during numerical imaging experiments with a–c) unknown and d–e) known dimer position. Red and blue colored regions correspond to plane wave and superoscillatory illumination, respectively, while red and blue solid lines mark the first and the third quartiles of the corresponding error distributions. The horizontal dotted lines indicate the average value of the IQRs over the range of the true values of the respective dimension. The vertical dotted lines in panels (a) and (b) indicate the geometric dimension's true value below which the network returns predominantly negative, nonphysical values. f) Dependence of resolution (in dimer gap B) as a function of the dynamic range of the photodetector.

Figure 4

DSTM proof‐of‐principle experiment. a,b) The statistical distribution of the retrieved results for the width of the a) dimer component A and b) the dimer gap B presented as the difference between the retrieved value and the true value as measured with scanning electron microscope. Blue lines correspond to results obtained with superoscillatory illumination, while red lines correspond to broad Gaussian illumination. The histogram is calculated from retrieved parameters corresponding to 500 different realizations of the neural network.

Figure 5

Sensitivity of far‐field intensity patterns on the presence and position of an absorbing nanoparticle that is λ/1000 in size. a,c) Normalized change of the scattered field intensity profile caused by presence of the nanoparticle. b,d) Normalized change of the scattered field intensity profile caused by shifting the nanoparticle in steps of λ/2000 along the x direction. Panels (a) and (b) correspond to plane wave illumination; panels (c) and (d) illustrate illumination with a superoscillatory field. Maps (e) and (f) show intensity and phase profiles of the illuminating superoscillatory field, where light propagates along the positive z‐axis.