On-chip TIRF nanoscopy by applying Haar

Supplemental Document

On-chip TIRF nanoscopy by applying Haar

wavelet kernel analysis on intensity fluctuations induced by chip illumination: supplement

N

J

,

Ø

I. H

,

K

A

,

AND

B

S

A

1Department of Physics and Technology, UiT The Arctic University of Norway, Tromsø 9037, Norway

2Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

3nik.jay.hil@gmail.com

4balpreet.singh.ahluwalia@uit.no

This supplement published with The Optical Society on 9 November 2020 by The Authors under the terms of theCreative Commons Attribution 4.0 Licensein the format provided by the authors and unedited. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Supplement DOI:https://doi.org/10.6084/m9.figshare.13077950 Parent Article DOI:https://doi.org/10.1364/OE.403804

On-chip TIRF nanoscopy by applying Haar wavelet kernel analysis on intensity fluctuations induced by chip illumination : supplemental document

S1. HAWK transform

Consider the situation of a single pixel which has an intensity trace of 4 frames. This data stack of 4 frames in general may be represented as . The corresponding transformed

intensity trace can be obtained after multiplication with a 4×4 Haar matrix as shown below.

1 2

1 2

1 2

1 1 2

2 1 2 −1

2 −1 1 2

√2 − 1

√2 0 0

0 0 1

√2 − 1

√2

=

+ + + + − −2

−2

√2−

√2

=

The next step is to apply the desired filter level m. The possible values of m are integers in the range 1 to log , where N is the total number of frames in the original data stack.

The filtered pixel intensity trace can be calculated by applying the condition = to get the resultant vector

12 34

. 1

2 1 2

1

√2 0

1 2

1 2 − 1

√2 0 1

2 −1

2 0 1

1 √2 2 −1

2 0 − 1

√2

=

2+2+ /√2 2+

2− /√2 2−2+ /√2 2−2− /√2

= 12 3 4

=

For m = 1 the resultant vector is:

1 2 34

=

( − )

−( − )2 ( − )2

−( − )2 2 For m = 2 the resultant vector is:

12 34

=

( + )

4 −( + ) ( + ) 4

4 −( + )

−( + ) 4

4 +( + )

−( + ) 4

4 +( + ) 4

The resultant vectors are then appended together to get the HAWK processed data stack.

HAWK plugin in Fiji takes the desired filter level m as input from the user. After processing using HAWK, the negative values in the processed data stack are redressed positive or the positive and negative values are separated into two stacks and negative values are redressed positive. For the experiments presented in this manuscript, the latter condition is chosen with filter level = 3.

S2. A simple numerical example to illustrate the effect of the transform levels of HAWK

To understand the influence of HAWK on the original image stack, consider a temporally varying signal such as =

10010 1512

. This intensity trace is an example of a pixel lying on the border of a bright-dark band of the MMI pattern. The intensity trace of a pixel over time varies in proportion with the illumination intensity as the MMI pattern shifts transversally. The transformed traces for this particular pixel are

45

−451.5

−1.5 for

= 1 and 20.75 20.75

−20.75

−20.75

for = 2. It can be seen that if the original data stack is used for SOFI reconstruction, this particular pixel will be rendered dim in the SOFI reconstructed image compared to pixels lying on a bright fringe. But after processing with HAWK the transformed intensity trace can lead to a higher pixel value in the SOFI reconstructions thereby aiding in alleviating the reconstruction artifacts due to the MMI pattern.

Similarly, an emitter lying on a bright band of the MMI pattern over the entire sequence of four frames can be represented as

10086 9590

. This corresponds to an emitter exhibiting fluctuations with low temporal frequency. The transformed traces for such a pixel are

−77

−2.52.5

for = 1 and 0.250.25

−0.25

−0.25

for = 2. The non-linear response of SOFI images to brightness is therefore reduced after HAWK which helps prevent masking of the weaker emitters.

Lastly, let us consider an emitter exhibiting high temporal fluctuations. It can be represented as

100 1695 10

. The corresponding transform traces are 42

−4242.5

−42.5

for = 1 and 2.75

−2.752.75

−2.75

for = 2. It can be seen that a highly fluctuating signal is represented pre- dominantly by = 1 filter while low temporal frequency information of emitters is retained by the higher order filter levels. Therefore, by appropriately choosing the filter level the artifacts generated by SOFI due to MMI patterns can be alleviated via HAWK processing. Ideally the correct filter level has to ensure that all the emitters get adequately represented in the reconstructed image.

S3. HAWK helps depopulate regions with higher fluorophore density and increases the fluctuations

The next challenge for SOFI is in reconstructing those regions of the sample, which have high fluorophore density. A high fluorophore density yields lower fluctuations, which in turn leads to a lower pixel value in the SOFI reconstructions. This is experimentally demonstrated by Fig. S1. For this particular experiment, Alexa Fluor 647 is coated on a Tantalum pentoxide waveguide surface. Images are acquired every 30 ms in epi- fluorescence mode. A region with a high density of fluorophores as shown in Fig. S1 is chosen and the ratio of standard deviation to average over 300 frames is calculated. The same data stack of 300 frames is then processed using HAWK and the ratio of standard deviation to average is again calculated. The filter level = 3 is chosen so as to match with the experimental particulars described in the main article. It can be seen that the ratio of standard deviation to average increased two orders of magnitude for this experiment after the application of HAWK.

Fig. S1: Influ deviation ove frames after H standard devia

While ima SOFI reco molecules To see wh uniform lay imaged as d In the first frames wer only due t presented i oscillated a intensity tra due to the oscillating

uence of HAWK er 300 frames. (c

HAWK processin ation to average o

ging in wave onstruction m as well as du hich effect d yer of Alexa described in S t experiment, re acquired. I to the intrins in Fig. S2. Fo and a sequen ace of the pix intrinsic pho nature of the i

K on densely pa ) Ratio of standa ng. (e) Standard of 1778 frames ge

eguide TIRF m may arise fro

ue to the oscil dominates, the

Fluor 647 is Section 2.1 of the coupling It means that

ic photokinet or the second nce of 300 im xels in the ima otokinetics of illumination. T

acked fluorophor ard deviation to

deviation of 177 enerated using HA

mode, the flu m the intrin lating nature e following t s coated on a the main text.

g objective wa the fluctuatio tics of the fl d experiment, mages were ac

age frames so f the fluoresc The experime

res. (a) Average average over 30 78 frames genera AWK. Scale bar

uctuations nec nsic photokin

of the illumin two experime a Tantalum p

.

as held statio ons recorded luorescent mo the coupling cquired durin recorded will cent molecule ental results ar

e of 300 frames 0 frames. (d) Av ated using HAWK

8 μm.

cessary for pe etics of the nating scheme ents were pe pentoxide wav onary and a st in the image olecules. The g objective wa ng this proces l have fluctuat es as well as re presented in

. (b) Standard verage of 1778 K. (e) Ratio of

erforming a fluorescent e employed.

erformed. A veguide and tack of 300 e stack arise results are as manually ss. Now the tions arising due to the n Fig. S3.

Fig. S2: Fluct frames. (b) St stack of 300 deviation ove 1778 frames.

It is seen increased a can be see because of

Fig. S3: Fluc image of 300 original data s

tuations due to in tandard deviation frames. (d) Aver r 1778 frames. ( Scale bar 8 μm.

from Fig. S2 after the applic en from Fig.

the oscillating

tuations due to i frames. (b) Stan stack of 300 fram

ntrinsic photokine n over 300 frame

rage TIRF image f) Ratio of stand

2(c) and S2(f cation of HAW

S2(c) and Fig g illumination

intrinsic photokin dard deviation ov mes. (d) Average

etics in waveguid s. (c) Ratio of st e of HAWK proc dard deviation to

f) that the ra WK on the ori g. S3(c) that n scheme empl

netics and oscilla ver 300 frames. ( TIRF image of H

de TIRF mode. ( tandard deviation cessed data stack

average of the H

atio of standa iginal data stac the fluctuatio loyed.

ating nature of i (c) Ratio of stand HAWK processed

a) Average TIRF n to average of th k of 1778 frames HAWK processed

ard deviation ck of 300 fram ons have bee

llumination. (a) dard deviation to d data stack of 17

F image of 300 he original data s. (e) Standard d data stack of

to average mes. Also, it en enhanced

Average TIRF average of the 778 frames. (e)

Standard devi stack of 1778

The infere fluctuations seen that H waveguide shown in F uniformly fluctuations reconstruct S4. Effect quality

Fig. S4: Influe HAWK data s HAWK data s

Fig. S4 por that the HA low filter le explained i get adequat above we e predominan scaling of S

iation over 1778 frames. Scale ba

ences from th s arising due t HAWK help

TIRF imagin Fig. S1. It me

illuminated s even in regi tion artifacts o t of differen

ence of HAWK f stack with m = 1 stack with m = 4

rtrays the effe AWK data sta

evels such as in Section 1.2 tely represente expect the emi ntly represent SOFI. In this m

frames. (f) Ratio ar 8 μm.

hese experim to photokineti s in increasin ng mode and eans that the n

image can ions having h of SOFI due to t transforma

filter levels on 4^th 1, (b) HAWK da 4. Scale bar 8 μm.

ect of HAWK ack with m = m = 1, the hi 2. At higher f

ed in the imag itters exhibitin ed after the SO manuscript, m

o of standard dev

ments is that ics and waveg ng the ratio d in regions w

necessity of a be exploited high density o o MMI pattern ation levels

h order SOFI reco ata stack with m

.

filter levels o

= 3 gave the b igh temporal f filter levels, th ge stack. At ev ng low tempo OFI reconstru m = 3 gave the

viation to average

in waveguid guide illumina of standard with high de averaging out d by HAWK of fluorophore

ns.

of HAWK o

onstruction. 4^th or

= 2, (c) HAWK

on SOFI recon best 4^th order frequency con he low frequen ven higher filt oral frequency uctions due to e best reconstr

e of the HAWK

de TIRF imag ation are prese

deviation to ensity of fluor the modes to K to enhanc es, thereby all

on the recon

der SOFI reconst data stack with

nstructions. It SOFI recons ntent is more d

ncy informati ter levels like y with high int the non-linea ruction.

processed data

ging mode, ent. It is also

average in rophores as o generate a ce intensity

eviating the

nstruction

tructions on (a) m = 3 and (d)

can be seen struction. At dominant as on will also m = 4 and tensity to be ar brightness

S5. Effect Fiji plugin

Fig. S5: Ratio data stack wi enclosed by th μm.

t of the meth n on SOFI re

o of standard dev th ‘‘separate’’ op he yellow box, (d

hod of sepa econstructio

iation to average ption used. 4^th o d) HAWK data s

aration of ne on

on (a) HAWK d order SOFI recon tack enclosed by

egative value

data stack with ab nstruction carried y the red box. Sca

es available

bsolute option use d out on (c) HAW

ale bars: (a-b) 8 μ

e in HAWK

ed, (b) HAWK WK data stack μm and (c-d) 4

Fig. S6: Loca SOFI reconstr b-SOFI recon computed for reconstruction with b-SOFI Scale bar: 8 μ

al FRC resolution ruction on HAWK nstruction of orig r 100 × 100 pix n overlaid. The lo reconstructions.

μm.

n for the data of F K data stack. (c) ginal data stack w xels on b-SOFI ocal FRC images The pure white p

Fig. 7. (a) b-SOFI Local FRC reso with b-SOFI rec reconstruction o s are rescaled usin

pixels indicate re

I reconstruction o lution R(nm) com onstruction over f HAWK data s ng bilinear interp egions where loc

of the original da mputed for 100 × laid. (d) Local F stack with b-SO polation before ov cal FRC failed to

ata stack. (b) b-

× 100 pixels on FRC resolution FI on HAWK verlaying them o give a value.