017 nd International Seinar on Applied Physics, Optoelectronics and Photonics (APOP 017) ISBN: 978-1-60595-5-3 Structured Illuination Super-Resolution Iaging Achieved by Two Steps based on the Modulation of Background Light Field Chu-yi CHEN, Yan TANG, Li-xin ZHAO, Jun-bo LIU, Zhong-ye XIE, Yi ZHOU ABSTRACT Structured illuination icroscopy can break diffraction liit by odulating frequency of object. However, to decode spectru, conventional structured illuination super-resolution iaging technique needs to acquire three iages at least with different phases. Not only higher requireent is put forward to phase shift accuracy, but also reconstruction efficiency is badly affected. A ethod for achieving structured illuination super-resolution iaging by two steps based on background light field odulation is proposed in the paper. By odulating background light field and structured illuination light field without phase shift can extract the high frequency and achieve super-resolution iaging. The ethod iproving construction efficiency as well as reducing syste coplexity. INTRODUCTION Structured illuination icroscopy (SIM) is inspired by oiré effect. The high frequency inforation of the object is odulated into the low frequency region so as to through the diffraction liited syste. SIM can break the 1/ wavelength diffraction liit and double the syste resolution. Since 000, SIM is proposed by M.G.L, GUSTAFSSON who fro the University of San Francisco, this ethod attracted the researchers attention quickly by virtue of its siple device, and the object to be easureent has no special requireents. Dan Dan, who fro Xi an Institute of Optics and Precision Mechanics, Chinese Acadey of Sciences, proposed DMD-based LED-illuination Super-resolution and optical sectioning icroscopy in 01. All the conventional SIM ethods are to odulate high frequency part of the object beyond the diffraction liit into the range of the diffraction liited syste by loading the sinusoidal illuination light field on the object. In the process of reconstructing super-resolution iages, the spectru separation algorith is the key First author, Chu-yi CHEN, The Institute of Optics and Electronics, The Chinese Acadey of Sciences, Optical electrical avenue no.1,shuangliu district, Chengdu, Sichuan, China Second author, Tang YAN, The Institute of Optics and Electronics, The Chinese Acadey of Sciences, Chengdu, Sichuan, China. 140
to guarantee the quality of iaging. The conventional ethods require accurate phase shift. And when separate ultiple direction spectru, each direction requires at least three iages with different phases, greatly affected the reconstruction efficiency. steps based on background light field odulation is proposed in this paper. By using the background light field iage and the structured light odulation iage, the spectru of the object is separated by the specific algorith to extract the high frequency inforation. Then the super-resolution iage can be reconstructed. Copared with the conventional ethods, the ethod we proposed only needs to acquire two iages in one direction, not only reduces the requireent of phase shift accuracy, but also iproves the reconstruction efficiency. Especially when reconstructing ultiple directions spectru. For exaple, if you load three directions of structured light, the conventional ethod need to acquire at least nine iages. But the ethod proposed in this paper besides one background light field iage, each direction only need to acquire one structured light odulation iage. That is, only need four iages altogether can achieve super-resolution iaging. The efficiency of reconstruction is iproved greatly. THEORY steps based on background light field odulation is proposed in this paper. First, without structured light, the background light field can be expressed as g ( r ). The high frequency coponent of the object is filtered because of the diffraction liited syste. As shown in Fig.1. The dashed box represents the frequency range that the diffraction liited syste can receive. The spectru inside the dashed box can be expressed as ( ) = ( ) (1) g0 r g r h( r) where h( r ) is point spread function(psf), represents convolution. Figure 1. Object spectru distribution. Then loading the structured illuination on object, the structured light field iage that iage acquisition syste acquires can be expressed as g1 ( r) = [ g ( r) I( r)] h( r) () 141
where I( r) = I0[1+ cos( π p r + ϕ)] is intensity of illuination, is the average intensity of the structured light, is odulation, p is spatial frequency,ϕ is Initial phase. According to the Euler equation,forula can be rewritten as g1 ( r) = I0 [ g( r) 1+ exp ( iπ pr ) exp ( iϕ ) + exp ( iπ pr ) exp ( iϕ ) ] h( r) Fourier transfor of forula 3 G1 ( k) = I0[ G( k) + exp( iϕ) G( k p) + exp( iϕ) G( k + p)] H( k) = I0[ G( k) H( k) + exp( iϕ) G( k p) H( k) + exp( iϕ) G( k + p) H( k)] = I0[ G0 ( k) + exp( iϕ) G( k p) H( k) + exp( iϕ) G( k + p) H( k)] (3) (4) Figure. Distribution of spectru odulated by structured illuination. To extract the high frequency inforation, we odulate the background light field by the sae structure light. The iage can be expressed as g ' r = g r I( r) = g r h( r) I( r) (5) ( ) ( ) ( ) 0 0 According to the Euler forula, Fourier transfor of forula 5 is G0 '( k) = I0[ G0( k) + exp( iϕ ) G0 ( k p) + exp( iϕ ) G0 ( k + p)] (6) The spectru is shown in the dashed box below, and the dashed box represents the frequency range that the diffraction liited syste can receive. The spectru contains three parts, the frequency is at 0, p, p. As is shown in Fig.3. Figure 3. Spectru distribution of background light field loaded structured illuination. The zero order spectru that can through the diffraction liited syste is the sae. Therefore, the high-frequency coponents can be extracted by subtracting the 14
two spectru represented by the forulas 4 and 6, as shown in Fig.7 and 4. G0 '( k ) G1( k ) = I 0[ exp( iϕ )( G0 ( k p) G ( k p) H ( k )) + exp( iϕ )( G0 ( k + p) G ( k + p) H ( k ))] (7) Figure 4. High frequency part. ake Gw+ ( k + p) = G( k + p) H ( k), Gw ( k p) = G( k p) H ( k), the high-frequency inforation can be expressed as G( k + p) + = I0{ exp( iϕ )[ G0 ( k + p) Gw+ ( k + p)]} (8) G( k p) = I0{ exp( iϕ )[ G0 ( k p) Gw ( k p)]} (9) Move it to the correct position respectively. The ove distance and direction depend on the frequency and direction of structured light. The high-frequency coponent can be expressed as G( k) + = I0{ exp( iϕ )[ G0 ( k) Gw+ ( k)]} = kw[ G0 ( k) Gw+ ( k)] (10) G( k) = I0{ exp( iϕ )[ G0 ( k) Gw ( k)]} = kw[ G0 ( k) Gw ( k)] (11) where kw = I0 exp( iϕ ). Then add together the zero order spectru and the high frequency coponent can rebuild coplete spectral inforation G '( k) = G + G( k) / w + G( k) / w (1) The coplete spectru is shown in Fig.5 0 + Figure 5. Spectru reconstructed. SIMULATION ANALYSIS steps based on background light field odulation is proposed in this paper. The ethod has been siulated and analyzed. The object is an equidistant sine grating. As 143
shown in Figure 6. Using the low-pass filter to substitute for the diffraction liited syste. We can see that the high frequency region of the iage is blurred, that is, the high frequency inforation is lost, as is shown in Fig.7. Fig.8 is the spectru distribution of the object through the diffraction liited syste. Figure 6. Object. Figure 7. Iaging of object liited by diffraction. Load the structured light on the object. To extract high frequency coponent, odulate background light field by the sae structured light. Subtract the spectru of odulated background light field fro the spectru odulated by structured light. The result is shown in Fig.9. Figure 8. Spectru distribution of the object through the diffraction liited syste. Figure 9. Subtracting spectru of odulated background light field fro spectru odulated by structured illuination. Move the high frequency coponent to original position and add it to the zero order spectru to rebuild coplete spectru. The rebuild resultant is shown in Fig.10. The coparison of rebuild spectru and object spectru is shown in Fig.11. 144
Figure 10. Iage restored. CONCLUSION Figure 11. Spectru coparison of reconstruction resultant and saple. Blue is the spectru of reconstruction resultant, and the red is the spectru of saple. steps based on background light field odulation is proposed in this paper. Siulation and experient verify, the ethod can achieve super-resolution iaging only by using two iages. Without accurate phase shift, we can extract the high frequency coponent, rebuild the coplete frequency doain inforation. Not only reduces the coplexity of the syste, but also iprove the efficiency of reconstruction. Especially for ulti-directional structured light, the nuber of iages will be greatly reduced, the advantage of efficiency of reconstruction is ore obvious. ACKNOWLEDGEMENT The article was supported by the project of National Natural Science Foundation of China.(Grant No. 6167506, 616051, 61604154). REFERENCES 1. Scherelleh L, Heintzann R, Leonhardt H. A guide to super-resolution fluorescence icroscopy, Journal of Cell Biology, 010, pp. 165-175.. Wu Meirui, Yang Xibin, Xiong Daxi et al. Structured Illuination Fluorescence Microscopy: Diffraction-Liit Breaking Principle and Application in Life Science, Laser & Optoelectronics Progress, 015 (5), pp. 010003-1 - 010003-11. 3. Abbe E. Beiträge zur Theorie des Mikroskops und der ikroskopischen Wahrnehung, Archiv für ikroskopische Anatoie, 1873(9), pp. 413-418. 4. M. G. L. Gustafsson. Surpassing the lateral resolution liit by a factor of two using structured illuination icroscopy, Journal of Microscopy, 000(198), pp. 8-87. 5. D. Dan, Lei Ming, Yao Baoli et al. DMD-based LED-illuination Super-resolution and optical sectioning icroscopy, Scientific Reports, 013(3), pp. 1-7. 6. Wu Meirui. Research on Structured Illuination Fluorescence Microscopy Iaging Syste, Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Acadey of Sciences, 014, p. 15-19. 145