Fabrication and characterization of modulation masks for multimodal spatial frequency modulated microscopy

Nathan Worts; Michael Young; Jeff Field; Randy Bartels; Jason Jones; Jeff Squier

doi:10.1364/AO.57.004683

1. INTRODUCTION

A. General Introduction

Multi-modal nonlinear spatial frequency modulated imaging (SPIFI) allows an optical microscope to achieve enhanced resolution [1] over fields of view that extend from hundreds of micrometers to millimeters. This enables the user to push boundaries in terms of understanding structure and function, whether it involves biological systems or a platform designed to investigate the physics of a material. The near infrared (NIR) wavelengths (700–1500 nm and beyond) used as the excitation source help optimize penetration depths, an especially significant property when imaging within scattering specimens such as brain tissue [2]. Localization of the multiphoton signal within the focal volume facilitates single-element detection, e.g., with a photomultiplier tube (PMT) or photodiode. This collection method is important for optimizing the image signal-to-noise ratio (SNR) as the signal photons are detected independent of the number or location of scattering events that may occur as they propagate through and exit the specimen on the way to the collection optics.

SPIFI satisfies the important criteria of (1) extended excitation sources for effective acquisition rates, especially important with the ever-increasing demands for a wider field of view; (2) supports single-element detection for image optimization, significant when imaging within a scattering environment; and (3) all the while provides the ability to push the image resolution in multiple linear and nonlinear imaging modalities. To date, SPIFI has been used to image in conjunction with a variety of contrast mechanisms including the fundamental excitation wavelength, second harmonic generation (SHG) and third harmonic generation (THG), and two-photon excitation fluorescence (TPEF) [3,4]. This imaging technique has also been utilized in various other modalities including tomographic imaging [5–7], fluorescent holographic imaging [8,9], in addition to hyperspectral imaging [10,11].

SPIFI utilizes a cylindrical lens to focus the excitation beam to a line, creating a sheet of light. The light sheet then interacts with a specifically designed mask that modulates the intensity of each resolvable pixel across the light sheet at a different frequency. The modulated line focus is then image relayed (typically with demagnification) to the focal plane of the microscope objective. This results in a projection of time varying spatial frequencies onto the sample [9]. The generated signal light from the desired linear or nonlinear process is collected by an objective lens either in a transmission or epi-detection geometry. All these signal photons are directed to a single-element detector such as a PMT or a photodiode. The resultant voltage versus time signal from the detector can then be Fourier transformed to yield a one-dimensional image. By modulation of the excitation source, in a strategic fashion, we have achieved one-dimensional imaging with single-element detection.

Significantly, Field et al. [1] demonstrated that one of the additional benefits of SPIFI imaging is extended resolution limits. Measurements and modeling demonstrated that for multiphoton imaging modalities in particular, an excitation process that scales as $I^{η}$ (where $I$ is the excitation intensity and $η$ is the order of the nonlinear process) results in spatial resolution gains up to $2 η$ below the diffraction limit. These results were achieved using a transmissive mask geometry created through lithography. The mask fabrication was performed commercially, with the cost and lead-time for the masks limiting the imaging system optimization process.

The intent of this work is to demonstrate the utility of using femtosecond laser plasma-mediated ablation processes as a method for mask fabrication with several advantages following. The process is in-house, facilitating rapid exploration of mask design and processing techniques. Second, it enables the material and geometry space to be expanded. For example, here we present for the first time to our knowledge both home-built reflective masks in rectangular geometries and transmission masks in polar geometries. Notably, prior to this work, it was not obvious that femtosecond plasma-mediated ablation could be effectively utilized over reflective or transmission surfaces to create a mask with sufficient modulation depth to support the imaging processes described here. The results quantified in this paper, however, show that in fact this is the case, which opens the door to creative, robust mask design with rapid turn around.

B. SPIFI Mask Geometry and Configurations

It is possible to implement the modulation pattern required for SPIFI in rectangular or polar coordinates. This makes the design extremely flexible. Rectangular coordinate masks can be fabricated on reflective substrates and are used when it is desirable to scan the excitation beam across the mask. Polar coordinate masks are desirable for transmission geometries. In this case, the excitation beam is stationary, and is simply transmitted through the mask as it rotates.

Starting by defining the $y$ position in the modulation pattern as

y (t) = ν_{y} t,

the modulation equation in rectangular coordinates is described by

m (x^{'}, y) = \frac{1}{2} + \frac{1}{2} \cos (2 π Δ k_{r} x^{'} y),

where

x^{'}

and

y

are the rectangular coordinates. We define the variable

κ_{r}

as

κ_{r} = Δ k_{r} ν_{y},

with

Δ k_{r}

being the spatial frequency parameter and

ν_{y}

the velocity in the

y

direction. It is also beneficial to define the lateral position

x^{'}

relative to the central position

x_{c}

,

x^{'} = x + x_{c} .

The carrier, or central frequency of the modulation, can be defined as

ω_{c} = 2 π Δ k_{r} ν_{y} x_{c},

which when substituting into the original modulation equation in Eq. (2) leads to the new form of the equation,

m (x, t) = \frac{1}{2} + \frac{1}{2} \cos (ω_{c} t + 2 π κ_{y} t x) .

To convert this continuous modulation equation to binary, the equation can be rewritten as

m (x, t) = \frac{1}{2} + \frac{1}{2} sgn (ω_{c} t + 2 π κ_{y} t x),

where the sgn function is defined to be 1 if the value of its argument is greater than or equal to the desired duty cycle of the mask and 0 if the argument is less than the value of the duty cycle. A key point of the optimized mask design is to realize that the mask diffracts the light sheet as it is reflected or transmitted. Consequently, the duty cycle of the binary mask has a significant impact on the diffracted orders. When describing the duty cycle with the variable

Δ

,

a_{j} (Δ) = Δ \frac{\sin (π Δ j)}{π Δ j}

shows which diffracted orders are enhanced and which are suppressed [12].

a_{j}

represents the coefficient of the diffracted order number j. The duty cycle chosen for this experiment was 50%, as it suppresses the second and fourth diffracted orders while maintaining a large coefficient in the first diffracted order. A simple visualization of this relationship is shown in Fig. 1.

Fig. 1. Diffracted order coefficient values as a function of the modulation mask duty cycle from Eq. (8). Vertical dashed line represents the 50% duty cycle used in this experiment.

Abstract

1. INTRODUCTION

A. General Introduction

B. SPIFI Mask Geometry and Configurations

C. SPIFI Mask Fabrication

1. Laser Machining System

D. Mask Substrates and Characteristics

E. Amplitude Modulation Capabilities of the Machined Masks

2. MICROSCOPE CONFIGURATIONS

A. Description of the Microscope Configurations

3. RESULTS AND DISCUSSION

A. Demonstration of Enhanced Resolution

1. Mask Diffraction

2. Enhanced Resolution Data

B. Transmission Mask Images

1. Laser Ablated Spots

C. Reflection Mask Images

1. Second Harmonic Generation Images

2. Third Harmonic Generation Images

3. Two Photon Excitation Fluorescence Images

4. CONCLUSIONS

A. General Conclusions

Funding

Acknowledgment

REFERENCES

Cited By

Figures (17)

Equations (16)

Applied Optics