s 2 stigmator: a closed-form solution for single-pass correction of TEM lens astigmatism

Transcription

1 s 2 stigmator: a closed-form solution for single-pass correction of TEM lens astigmatism Rui Yan, Kunpeng Li, Wen Jiang Purdue Cryo-EM Facility Markey Center for Structural Biology

2 TEM objective lens astigmatism The elliptical shape of Thon rings is an indicator of astigmatism. Astigmatism = 0 Defocus = 500nm Astigmatism = 100nm Angle = 30 Defocus = 500nm

3 Visual roundness method Very high magnification & very small defocus for astigmatism correction Lower magnification & larger defocus for data collection Power spectra of an image collected from CM200 (magnification = 200K, defocus ~100nm) Simulated power spectra Astigmatism = 50 nm Angle = 30 degree Defocus = 300 nm Simulated power spectra Astigmatism = 50 nm Angle = 30 degree Defocus = 1500 nm

4 s 1 power s 2 power s 1 power: increasing oscillations s 2 power: uniform oscillations Jiang et al., 2012

5 s 2 stigmator: a closed-form algorithm A B C D E F G I J H Yan et al., 2017

6 I 1 Single-pass tuning strategy I 2 Octupole stigmator Turn 1 st knob (M-Y or M-X) Step 1 Initial Turn 2 nd knob (M-X or M-Y) Step 2 Final Expected trajectory of the single-pass tuning strategy for astigmatism correction using s 2 stigmator Yan et al., 2017

7 Single-pass tuning strategy 7

8 Video: Single-pass tuning strategy

9 I 1 I 2 Arbitrary order of adjusting the two stigmators Octupole stigmator A:MY-MX trajectory B:MX-MY trajectory Step1: MY Step1: MX Step2: MX Step2: MY Screenshots of single-pass tuning strategy of astigmatism correction using s 2 stigmator

10 s 2 stigmator method Provides real-time feedback for astigmatism correction Enhances the sensitivity in ellipticity detection Prevents the bias and subjective results from operators Establishes an efficient single-pass tuning strategy, instead of blindly playing with the two stigmators Guides users to correct astigmatism at any magnification & defocus

11 Defocus-dependent astigmatism A B C D Titan Krios Increase Defocus Increase/Decrease Defocus Decrease Defocus E F G H CM200 Increase Defocus Increase/Decrease Defocus Decrease Defocus Yan et al., 2018

12 Defocus-dependent astigmatism ) V "#$ = V &'( ) = k &'( 2 I &'( /0 + V +, + V +- + V &'( Defocus-dependent astigmatism term 2 e &'( + k +, 2 I +, 2 e +, + k +- 2 I +- 2 e +- + k &'( 2 (I &'( I ) &'( ) 2 e &'( Scaling factor Unit vector V obj V sum = 0 Change of objective lens current when defocus is increased/decreased V MX V MY k: a scaling factor representing how strong the dependence is between V and I I: current e : a unit vector representing the direction of the lens astigmatism (V ) 12

13 Observations of defocus-dependent astigmatism in cryo-em data Yan et al., 2018

14 Origin of defocus/magnification dependent astigmatism Microscope alignment Before data collection High magnification Small defocus Data collection After astigmatism correction Low magnification A range of defocus V obj V sum = 0 V obj V sum 0 V MX V MX V MY V MY

15 Variability of defocus-dependent astigmatism A B C D Titan Krios Day1 Day2 Day3 E F G H CM200 Day1 Day2 Day3 V &'( = k obj 2 I obj 2 e obj Stochastic variations! Yan et al., 2018

16 Magnification-dependent astigmatism (Titan Krios ) A B C Measurement 1 Measurement 2 Measurement 3 D E F Yan et al., 2018

17 Recommendations for optimal TEM operations Instrument Alignment mag for instrument alignment = mag for data collection defocus for stigmation = median defocus of intended defocus range for data collection Data Collection mag of focus-mode = mag of exposure mode

18 Volta Phase Plate CTF fitting is harder for VPP images

19 s 2 ctf: defocus and phase are decoupled CTF s K = sin (2π( fλ 2 sk + C "λ T 4 sv ) + φ) Phase Shift: S 2 Simulation S 1

20 φ = 0 φ = 45 φ = 90 φ = 135 FFT(S 2 ) 20