How To Measure FWHM from Image Python

Importing Python Libraries

The main libraries we will use are:

import numpy as np 
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from skimage import io, filters

• NumPy: Provides arrays and mathematical operations
• Matplotlib: Visualization and plotting
• SciPy: Curve fitting and optimization
• scikit-image: Image processing and analysis

Loading the Image

We will work with a sample microscope image, but the process is adaptable to any image.

image = io.imread('sample_image.jpg') 

• Many common image formats supported
• Image loaded as NumPy array

Visualizing the Image

Use Matplotlib to display the image:

fig, ax = plt.subplots()
ax.imshow(image, cmap='gray')

• cmap=’gray’ sets grayscale color mapping
• Can zoom in on features of interest

Applying Filters

Use scikit-image to filter and enhance image:

image_filtered = filters.gaussian(image, sigma=2)
edges = filters.sobel(image_filtered)

• gaussian reduces noise
• sobel detects edges

Select Profile Cross Section

row_num = 300 # Select row number
profile = edges[row_num, :] # Extract row intensities

• Profile contains intensity values along cross section
• Can visualize profile as line plot

Plot Profile

plt.plot(profile) 
plt.xlabel('Pixel Number')
plt.ylabel('Intensity')

• Profile intensities now visualized
• Can inspect peaks representing edges

Fit Gaussian Curve

Use SciPy curve fitting to fit Gaussian model:

mean = len(profile) / 2 # Estimate center position

def gaussian(x, amp, cen, wid):
    return amp * np.exp(-(x - cen)**2 / wid)

popt, pcov = curve_fit(gaussian, range(len(profile)), profile, p0=[1, mean, 1])

• gaussian defines model function
• curve_fit determines optimal parameters
• popt contains best fit parameters

Calculate FWHM

The width parameter represents the standard deviation $\sigma$.

fwhm = 2 * np.sqrt(2 * np.log(2)) * popt[2] 
print(f'FWHM: {fwhm:.2f} pixels')

• FWHM is 2.355$\sigma$ for Gaussian function
• Print FWHM value from fitted width

Overlay Fit on Profile

x = np.arange(len(profile))  
y = gaussian(x, *popt) 

plt.plot(x, profile)
plt.plot(x, y, '--')
plt.xlabel('Pixel Number')
plt.ylabel('Intensity')

• Overplots fitted Gaussian curve
• Matches selected peak nicely

Consider Multiple Peaks

Above examines single peak, but should consider full image:

• Repeat process with multiple row and column cuts
• Can automation with loops through coordinates
• Take average as overall FWHM assessment

Summary

In this guide we covered key steps for measuring FWHM from images in Python:

📌 Load image and filter noise
📌 Take cross sectional intensity profile
📌 Fit Gaussian curve to peaks
📌 Calculate FWHM from fitted width
📌 Analyze multiple profiles for robust measurement

Being able to quantify feature sizes like FWHM enables resolution comparison across image sets and systems. The Python-based workflow presented here provides an accessible way to conduct this important analysis.