Before doing either, you must ensure your image is calibrated.

Step 0: Calibrate your image
If your image doesn't already have physical units (nm or Å) embedded in its metadata, you need to set the scale using the scale bar on the TEM image.

1. Select the Straight Line tool.
2. Draw a line exactly over the scale bar in your image.
3. Go to Analyze > Set Scale...
4. Enter the known distance of the scale bar in the Known distance box, and set the Unit of length (e.g., nm).
5. Check Global if you want this scale applied to other images you open. Click OK.

Method 1: The Profile Plot (Real Space)
This method is highly visual and great for a quick measurement. The golden rule here is never measure just one fringe, as it introduces massive human error. Always measure across multiple fringes and average them.

1. Select the Straight Line tool.
2. Draw a line perpendicular to the lattice fringes, crossing as many clear fringes as possible (e.g., 10 fringes).
3. Go to Analyze > Plot Profile (or press Ctrl+K / Cmd+K).
   A graph will pop up showing the peaks and valleys of the pixel intensity. Each peak is a lattice plane.
4. Measure the total distance L from the first peak to the last peak.
5. Count the number of gaps (fringe spacings) between those peaks, let's call this n.
6. Calculate the d-spacing using the formula:
   d = L/n

Method 2: The FFT Method (Reciprocal Space)
This is the most accurate and professionally accepted method for HRTEM analysis. It averages the spacing over the entire selected area, eliminating local distortions or measurement errors.

1. Use the Rectangle Tool to select a clean, square region of your lattice fringes.
2. Go to Process > FFT > FFT. A new window will open showing a central bright spot with symmetrical spots around it.
3. Select the Straight Line tool.
4. Draw a line from the exact center of the central bright spot to the exact center of one of the outer diffraction spots.
   Tip: To be even more accurate, draw a line connecting two opposite outer spots (passing through the center) and divide the final length by 2.
5. Go to Analyze > Measure (or press Ctrl+M / Cmd+M).
   Look at the Length value in the Results window. Because the FFT is in reciprocal space, the distance you measured is the reciprocal vector R.
   If ImageJ automatically converted the FFT axes to real-space units (which it often does if calibrated), the length might already be your d-spacing. If the axes are in reciprocal units (1/nm), ,you calculate the d-spacing as:
   d=1/R

Shortcut trick: If your image is properly calibrated, simply hover your mouse cursor over the center of an outer diffraction spot in the FFT window. Look at the ImageJ status bar (the text right below the toolbar). It will often display the
d-spacing directly as d=... nm!

Here are the most effective methods to denoise TEM images in ImageJ, ordered from the simplest to the most advanced.

1. The Median Filter (Best for general noise)
   If your image looks grainy (salt-and-pepper noise), the Median filter is usually your best first step. Unlike a Gaussian blur, which softens everything, the Median filter removes noise while preserving the sharp edges of your nanoparticles, cells, or grain boundaries.

How to do it: Go to Process > Filters > Median...
Settings: Set the Radius to a small number (start with 1 or 2 pixels). Check the "Preview" box to see the effect in real-time. If you set the radius too high, you will start losing actual structural details.

2. FFT Bandpass Filter (Best for HRTEM / Lattice fringes)
   If you are doing High-Resolution TEM (HRTEM) and want to see atomic lattice planes more clearly, Fast Fourier Transform (FFT) filtering is the standard method. It separates the periodic signal (the crystal lattice) from the random noise (amorphous carbon or detector noise).

How to do it: Go to Process > FFT > Bandpass Filter...
Settings:
Filter large structures down to: Filters out uneven background illumination (set this to a value larger than your lattice spacing, e.g., 40 pixels).
Filter small structures up to: Filters out high-frequency random noise (set this to a value smaller than your lattice spacing, e.g., 3 pixels).
Suppress stripes: Choose "None" unless you have specific scanning artifacts.

3. Manual FFT Masking (For isolating specific crystal planes)
   If the Bandpass filter isn't precise enough, you can manually select the diffraction spots in reciprocal space to perfectly isolate your crystal lattice.

Go to Process > FFT > FFT. A new window will open showing the diffraction pattern.
Select the Brush Tool or Oval Tool from the ImageJ toolbar.
Draw over the bright diffraction spots (and the central spot) to select them.
Go to Edit > Clear Outside (this turns everything except your spots to black, effectively deleting the noise).
Go to Process > FFT > Inverse FFT. The resulting image will be a beautifully clean reconstruction of your lattice.

4. Subtract Background (For uneven illumination)
   Sometimes the "noise" is actually a gradient where one side of the TEM grid is thicker or darker than the other.

How to do it: Go to Process > Subtract Background...
Settings: Use the Rolling ball radius. The trick is to set this radius to be larger than the largest object of interest in your image. For example, if your nanoparticles are 50 pixels wide, set the radius to 100 pixels. This ensures it only removes the background gradient and doesn't hollow out your particles.
A quick warning on Gaussian Blur
You can use Process > Filters > Gaussian Blur, but use it with extreme caution. It averages the pixels together, which reduces noise but also blurs the edges of your features. It is generally frowned upon for quantitative TEM analysis because it destroys high-resolution data.