How can I turn time series data into a spatial map?

Motivation: I am building a microscope to scan a laser across patterned surfaces to map the surface. The most intuitive method for this is to step from one point to the next and collect data at each fixed point. However, this is very slow. The fastest method is to use continuous motion of the laser spot to create a time series of data that has associated X,Y points at each time. However, real experimental equipment can't follow an arbitrary path due to finite accelerations (i.e., PID settings). This means that a raster map (see blue line in plots) will have errors in the true position compared to the target position when rastering quickly (see red line in plots). This in itself is not a problem as long as the visualized data accounts for the true position of the measured data.

Problem: The problem is visualization of the resulting "map". Specifically, time series data can't be easily converted into a 2D matrix that can be plotted in the "surf" function to visualize the surface map/image. This is even more complicated when using non-rastering mapping methods such as Lissajous motion.

Need:

1. A surface plotting function that accepts vectors for X,Y and Z instead of 2D arrays. Similar to "plot3" but that yields a "continuous surface like "surf". OR
2. A way to sort/rearrange time series data into a 2D matrix that can be used in "surf" or other similar surface plotting function.

Data Included:

1. Target points vs. time
2. Measured position vs. time

Answer 1

[Christopher Saltonstall]

Answer: Use "griddata" and "meshgrid" functions as shown below.

clear

close all

%% Get experimental data

path = 'C:\';

filename = 'data.mat';

load(fullfile(path,filename));

%down sample factor

fsample = 30;

%number of x-mesh points

nx = 100;

%number of y-mesh points

ny = 100;

% time vector (s)

t = data.measure.t;

t = downsample(t,fsample);

% x-position vector (um)

x = data.measure.x;

x = downsample(x,fsample);

% y-position vector (um)

y = data.measure.y;

y = downsample(y,fsample);

%% generate z-data using experimental data points for visual example

% x-wavelength

Lx = 10;

% y-wavelength

Ly = 6;

% z-points for heat map

z = sin(2*pi/Lx*x) + cos(2*pi/Ly*y);

%% Choose mesh points

xmin = min(x);

xmax = max(x);

ymin = min(y);

ymax = max(y);

%sample points for mesh

xSample = linspace(xmin,xmax,nx);

ySample = linspace(ymin,ymax,ny);

%2D array of x and y points

[xMesh, yMesh] = meshgrid(xSample,ySample);

%interpolate z-data using mesh points

zMesh = griddata(x,y,z,xMesh,yMesh,'cubic');

%% Plot that ish

figure(1)

scatter3(x,y,z,5,z)

colormap(gca,"winter")

xlabel('x-Position (um)')

ylabel('y-Position (um)')

zlabel('Intensity (a.u.)')

title('3D Scatter Plot')

figure(2)

mesh(xMesh,yMesh,zMesh)

axis tight;

hold on

plot3(x,y,z,'.r','MarkerSize',5)

hold on

xlabel('x-Position (um)')

ylabel('y-Position (um)')

zlabel('Intensity (a.u.)')

title('Mesh + Scatter Plot')

figure(3)

h = surf(xMesh,yMesh,zMesh);

shading interp

set(h,'LineStyle','none')

xlabel('x-Position (um)')

ylabel('y-Position (um)')

zlabel('Intensity (a.u.)')

title('Surface Plot')