For measuring particle size, there are several free software options available, each with its own set of features and capabilities. Here are a few you might consider:

ImageJ: A popular open-source image processing program developed by the National Institutes of Health. It's widely used for analyzing particle sizes in images, especially in scientific research. ImageJ supports various image formats and provides tools for measuring and analyzing particle size distributions.

Gwyddion: This is a modular program for scanning probe microscopy data analysis but can also be used for analyzing particle sizes. It's open-source and provides a range of tools for data visualization and processing.

Scikit-Image: A collection of algorithms for image processing in Python. While primarily a library for Python, it's suitable for those comfortable with scripting and programming. It's useful for more complex or customized particle size analysis tasks.

Fiji: An extension of ImageJ, Fiji is “batteries-included” - meaning it has many plugins pre-installed for various image analysis tasks, including particle size analysis.

OpenCV: This is more of a computer vision library, but it can be used for particle size analysis if you have programming skills, particularly in Python, C++, or Java.

Each of these tools has its own learning curve and may require some background knowledge in image processing or programming. The choice of software often depends on the specific requirements of your analysis, the complexity of the images, and your comfort with programming or using specialized software tools.

You have following free software options:

1. ImageJ/Fiji: ImageJ is a popular open-source image analysis software that can be used for particle size analysis. Fiji is an extended distribution of ImageJ with additional plugins and functionalities. Both ImageJ and Fiji have a wide range of plugins available for particle size measurement and analysis.

2. ImageJ Particle Size Distribution (PSD) Plugin: This plugin is specifically designed for particle size analysis in ImageJ/Fiji. It provides various options for particle detection, measurement, and size distribution analysis. It can handle images from XRD, TEM, and SEM.

3. ImageJ Particle Tracker Plugin: This plugin is useful for tracking particles and analyzing their movement in time-lapse image sequences. It can be used to estimate particle size based on particle tracking and displacement analysis. It may be suitable for certain TEM or SEM applications.

4. Nano Measurer: Nano Measurer is a free software for particle size analysis, including nanoparticle size distribution, from TEM or SEM images. It provides various measurement tools and features, including particle detection, size measurement, and statistical analysis.

5. Image Analysis and Stereology (IAS) Toolbox: The IAS Toolbox is a comprehensive open-source software for image analysis and stereology. It includes functionalities for particle size analysis, including size measurement and size distribution estimation, from microscopy images such as TEM and SEM.

Hope it helps