Selective Plane Illumination Microscopy Setup for Volumetric Imaging

Kyiv, Ukraine

L-SPIM setup based on open source projects.

Samples and desired characteristics

NB: is 10x NA 0.25 FN 22 enough?

Sciatic nerve

• Nerve diameter: 1.5-2 mm
• Nerve length: 5-20 mm
• A-fiber diameter: 1.5 - 10 um
• C-fiber diameter: 0.5 - 2 um
• Minimal vessel diameter

Scaffolds

In progress

Characteristics

• FOV ~ 1x2 mm
• Lateral resolution <1.5 um

Design notes

Tip

Read more about the SPIM principles:

• Selective Plane Illumination Microscopy
• openSPIM project
• Selective plane illumination microscopy techniques in developmental biology
• Using tissue clearing and light sheet fluorescence microscopy for the three-dimensional analysis of sensory and sympathetic nerve endings that innervate bone and dental tissue of mice Olarte et al., 2018 Power and Huisken, 2017

Gaussian litgh sheet

Gaussian beam

Focusing of a Gaussian beam (Power and Huisken, 2022)

In paraxial approximation:

$$\sin \theta \approx \tan \theta \approx \theta$$

Accordng this approximation numerical aperture is equal:

$$NA = n \sin \theta \approx n \theta$$

Or for air:

$$NA = \theta \simeq \frac{d_{beam}}{2 f}$$

The Rayleigh range of the beam and beam waist:

$$\omega (x_R) = \sqrt{2} \omega_0$$ $$x_R = \frac{\pi \omega_{0}^{2}}{\lambda}$$

Static light sheet thickness:

$$\theta = \frac{\pi \omega_{0}}{\lambda} \Rightarrow \omega_0 = \frac{2 f \lambda}{\pi d_{beam}} \Rightarrow z_{ls} = 2 \omega_0 = \frac{4 f \lambda}{\pi d_{beam}}$$

Static light sheet length:

$$x_R = \frac{\pi \omega_{0}^{2}}{\lambda} \Rightarrow x_R = \frac{4 f^2 \lambda}{\pi d_{beam}^2} \Rightarrow x_{ls} = 2 x_{R} = \frac{8 f^2 \lambda}{\pi d_{beam}^2}$$

Illumination system

Relayed generation of a well-corrected static light sheet (Huisken et al., 2004)

Objective focal length ($f_{ref}$ for Olympus 180 mm):

$$f_{front} = n_{imm} f_{back}$$ $$f_{obj} = f_{back} = \frac{f_{ref}}{M}$$ $$d_{BFP} = d_{beam} \frac{f_{tube}}{f_{scan}}$$

Illumination NA:

$$NA_{ill} = n_{imm} \theta = \frac{d_{beam} n_{imm}}{2 f_{front}} = \frac{d_{beam}}{2 f_{obj}}$$

Static light sheet parameters:

$$z_{ls} = \frac{2 \lambda}{\pi NA_{ill}}$$ $$x_{ls} = \frac{2 n_{imm} \lambda}{\pi NA_{ill}^2}$$

Relay system:

$$\textbf{Z}_{ls} = z_{ls} \frac{f_{scan}}{f_{tube}} = \frac{4 f_obj \lambda}{\pi d_{beam}} \cdot \frac{f_{scan}}{f_{tube}}$$ $$\textbf{X}_{ls} = x_{ls} (\frac{f_{scan}}{f_{tube}})^2 = \frac{8 f_{obj}^2 n_{imm} \lambda}{\pi d_{beam}^2} \cdot (\frac{f_{scan}}{f_{tube}})^2$$ $$\textbf{Y}_{ls} = \frac{f_{scan}}{f_{cyl}} \frac{f_{obj}}{f_{tube}} d_{beam}$$

Detection arm

Lateral resolution (Rayleigh criterion):

$$d_{xy} = \frac{0.61 \cdot \lambda_{det.}}{NA_{det.}}$$

Axial resolution (depth of field/DOF):

$$d_z = \frac{n \cdot \lambda_{det.}}{NA_{det.}^2}$$

V0

Detection arm

Parameter	Value
Detection objective	Olympus PlaN 10x 0.25 FN 22 (F18)
Detection tube lens	F100
Magnification	~5.56x
Camera	Basler Ace 2R Pro (a2A5320-23umPRO)
Pixel size	0.493 μm/px
Field of view	2.62x1.49 mm
Theoretical resolution (500 nm)	1.220 μm
Theoretical depth of field (500 nm, n=1.33)	10.640 μm
Z-stack step (Sutter Instruments MPC-200 with MP225/M)	0.0625 μm/μstep (16 μstep/μm)

Excitation arm

Control software

License

This open-source project is released under the CERN Open Hardware License. Our aims are to promote open scientific hardware development and to share our engineering solutions.