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开关效应和单分子定位的结合可以实现样品的超衍射分辨成像, 双螺旋点扩展函数将单分子定位纳米分辨从二维扩展到了三维.本文对双螺旋点扩展函数的三维定位精度展开了探讨.首先, 基于费希尔信息量, 计算了双螺旋点扩展函数的无偏估计, 得出其理论定位精度, 并分析了光子数、背景噪声以及有效像元尺寸大小对其定位精度的影响; 其次, 基于单分子定位实验过程中对于数据分析通常采用的高斯拟合质心定位算法, 通过误差传递函数定律求得双螺旋点扩展函数的轴向定位精度.计算机模拟结果表明, 在光子数大于1000的条件下, 高斯拟合质心定位精度和费希尔信息量理论定位精度符合较好. 本文的讨论不仅为双螺旋点扩展函数的三维定位精度提供了理论依据, 同时也可为实验提供理论指导.The combination of switch effect and single molecule positioning can realize the sample super diffraction resolution imaging, and double helix point spread function will be a single molecular orientation nanometer resolution extending from two dimensions to three dimensions. In this paper, three-dimensional (3D) positioning accuracy of the double helix point spread function is discussed. First, the theoretical localization accuracy for an unbiased estimator of the double-helix point spread function is compared with that for 3D localization using Fisher information and the influences of localization accuracy including photon number, varying levels of background and pixel size are analyzed. Second, based on the localization algorithm of gaussian fitting, which is usually adopted in data analysis of single molecular orientation in the experimental process, the axial localization accuracy of double helix point spread function is obtained by the error transfer function law. Computer simulation results show that under the condition of more than 1000 photons in number, the positioning accuracy of gaussian fitting localization algorithm and theory localization accuracy of Fisher information are in good agreement. The discussion of the paper provides not only the theoretical basis for 3D positioning accuracy of double helix point spread function, but also the theoretical guidance for the experiment at the same time.
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Keywords:
- double helix point spread function /
- Fisher information /
- localization precision /
- gaussian fitting
[1] Chen D N, Liu L, Yu B, Niu H B 2010 Acta Phys. Sin. 59 6948 (in Chinese) [陈丹妮, 刘磊, 于斌, 牛憨笨 2010 59 6948]
[2] Holtzer L, Meckel T, Schmidt T 2007 Appl. Phys. Lett. 90 053902
[3] Toprak E, Balci H, Blehm B H, Selvin P R 2007 Nano Lett. 7 2043
[4] Pavani S R P, Thompson M A, Biteen J S, Lord S J, Liu N, Twieg R J, Piestun R, Moerner W E 2009 PNAS 106 2995
[5] Shtengel G, Galbraith J A, Galbraith C G, Lippincott-Schwartz J, Gillette J M, Manley S, Sougrat R, Waterman C M, Kanchanawong P, Davidson M W, Fetter R D, Hess H F 2009 PNAS 106 3125
[6] Piestun R, Schechner Y Y, Shamir J 2000 JOSA A 17 294
[7] Pavani S R P, Greengard A, Piestun R 2009 Appl. Phys. Lett. 95 021103
[8] Thompson M A, Lew M D, Badieirostami M, Moerner W E 2010 Nano Lett. 10 211
[9] Ober R J, Ram S, Ward E S 2004 Biophys. J. 86 1185
[10] Badieirostami M, Lew M D, Thompson M A, Moerner W E 2010 Appl. Phys. Lett. 97 161103
[11] Ram S, Prabhat P, Chao J, Ward E S, Ober R J 2008 Biophys. J. 95 6025
[12] Khonina S N, Kotlyar V V, Soifer V A, Honkanen M, Lautanen J, Turunen J 1999 J. Mod. Opt. 46 227
[13] Liu Z M 1981 Error and Interpretation of Data (Beijing: Atomic Energy Press) p21 (in Chinese) [刘智敏 1981 误差与数据处理(北京: 原子能出版社) 第21页]
[14] Chen D N 2010 Ph. D. Dissertation (Wuhan: Huazhong University Of Science And Technology) (in Chinese) [陈丹妮 2010 博士学位论文(武汉: 华中科技大学)]
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[1] Chen D N, Liu L, Yu B, Niu H B 2010 Acta Phys. Sin. 59 6948 (in Chinese) [陈丹妮, 刘磊, 于斌, 牛憨笨 2010 59 6948]
[2] Holtzer L, Meckel T, Schmidt T 2007 Appl. Phys. Lett. 90 053902
[3] Toprak E, Balci H, Blehm B H, Selvin P R 2007 Nano Lett. 7 2043
[4] Pavani S R P, Thompson M A, Biteen J S, Lord S J, Liu N, Twieg R J, Piestun R, Moerner W E 2009 PNAS 106 2995
[5] Shtengel G, Galbraith J A, Galbraith C G, Lippincott-Schwartz J, Gillette J M, Manley S, Sougrat R, Waterman C M, Kanchanawong P, Davidson M W, Fetter R D, Hess H F 2009 PNAS 106 3125
[6] Piestun R, Schechner Y Y, Shamir J 2000 JOSA A 17 294
[7] Pavani S R P, Greengard A, Piestun R 2009 Appl. Phys. Lett. 95 021103
[8] Thompson M A, Lew M D, Badieirostami M, Moerner W E 2010 Nano Lett. 10 211
[9] Ober R J, Ram S, Ward E S 2004 Biophys. J. 86 1185
[10] Badieirostami M, Lew M D, Thompson M A, Moerner W E 2010 Appl. Phys. Lett. 97 161103
[11] Ram S, Prabhat P, Chao J, Ward E S, Ober R J 2008 Biophys. J. 95 6025
[12] Khonina S N, Kotlyar V V, Soifer V A, Honkanen M, Lautanen J, Turunen J 1999 J. Mod. Opt. 46 227
[13] Liu Z M 1981 Error and Interpretation of Data (Beijing: Atomic Energy Press) p21 (in Chinese) [刘智敏 1981 误差与数据处理(北京: 原子能出版社) 第21页]
[14] Chen D N 2010 Ph. D. Dissertation (Wuhan: Huazhong University Of Science And Technology) (in Chinese) [陈丹妮 2010 博士学位论文(武汉: 华中科技大学)]
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