Aligning a linear and non-linear x-axis

I have a spectroscopy plot of two curves, one relating to wavelength and one to wave number.

Wavenumber = 1/wavelegnth, so the relation is non linear. I want to align the top x-axis with bottom x-axis so that the peaks of the two curves are displayed in line with each other. Is this possible?

This is my current code:

t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1,wl1,sol1,'-r','LineWidth',3)
ax1.XAxisLocation = 'bottom';
ax1.YAxisLocation = 'left';
ax1.XColor = 'r';
ax1.YColor = 'r';
set(ax1, 'xlim',[300 400])
xlabel('wavelength (nm)',FontSize=18)
ylabel('Absorption',FontSize=18)
hold on
ax2 = axes(t);

plot(ax2,wn1,sol1_adj,'-k','LineWidth',3)

set(ax2, 'xlim',[250000 333333])
ax2.XAxisLocation = 'top';
ax2.YAxisLocation = 'right';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlabel('wavenumber(m^-^1)',FontSize=18)
ylabel('Absorption',FontSize=18)
set(gca, 'XDir','reverse')

ax1.FontSize = 16;
ax2.FontSize = 16;

[Matt J]

Can't run your code. No input variables are provided.

[William Rose]

@Theo McCarthy,

Is there a factor-of-ten error in one of the x-axis scales? Consider the wavenumber and wavelength for the right-most peak in the figure you provided. The black (wavenumber) peak is at about 2.65e5 m^-1. This corresponds to 3.77e-6 m = 3770 nm. But the red (wavelength) peak is at about 377 nm.

Answer 1

[Cris LaPierre]

The axes you are plotting into are linear, so I think the best solution would be to plot both plots using wavelength, and then convert the labels of to top x axis to wavenumber using xticklabels. Note that xticklabels displays the label as a string, not a numeric, so you need to format your number so that it appears as you want. I use sprintf below for that purpose.

If you are particular about which wavenumbers are shown, you can set the tick locations using xticks. Just remember to set the tick location using wavelength, not wavenumber.

The code might look like this. The first part just reproduces the issue.

BTW, one of your axes is off by a factor of 10 based on the equation you have shared.

x1 = (300:10:400)*1e-9;
x2 = 1./x1;
y=rand(1,length(x1));

% current aproach to show the issue
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1,x1,y,'-r')
xlabel('Wavelength (m)')
ax1.XColor = 'r';
ax1.YColor = 'r';

ax2 = axes(t);
plot(ax2,x2,y,'k')
ax2.XAxisLocation = 'top';
ax2.YAxisLocation = 'right';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlabel('Wavenumber (m^{-1})')

ax1.XAxis.Exponent = -9;
ax2.XAxis.Exponent = 4;

Now here is the same plot but with the proposed solution

figure
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1,x1,y,'-r')
xlabel('Wavelength (m)')
ax1.XColor = 'r';
ax1.YColor = 'r';

ax2 = axes(t);
plot(ax2,x1,y,'--k')
ax2.XAxisLocation = 'top';
ax2.YAxisLocation = 'right';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlabel('Wavenumber (m^{-1})')

% desired wavenumber tick locations
wvnum = (3.3:-0.1:2.5)*1e6 % 1/m

wvnum = 1×9

1.0e+06 * 3.3000 3.2000 3.1000 3.0000 2.9000 2.8000 2.7000 2.6000 2.5000

% corresponding wavelength
wvlg_nmTk = 1./wvnum % nm

wvlg_nmTk = 1×9

1.0e-06 * 0.3030 0.3125 0.3226 0.3333 0.3448 0.3571 0.3704 0.3846 0.4000

ax1.XAxis.Exponent = -9;
xticks(ax2,wvlg_nmTk);
xticklabels(ax2,sprintf('%3.0f\n',wvnum/1e4)); % display in meters

[Anna]

Hi Cris, Can I please seek some help with the code to plot spectrum data? The top x-axis is a wavelength in nm and the bottom one is a wavenumber in cm^{-1}. The top axis should align with the bottom one so that the top one has smaller tick spacing in the infra-red region and bigger tick spacing in the UV range. Appreciate your guidance with this matter.

clear all; clc;

wavelength = 300:1600; % in nm
wavenumber = 1e7./wavelength; % in cm-1
data = rand(1, length(wavenumber));

figure;
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1, wavenumber/1e3, data, '-r')
set(gca, 'XDir','reverse')
xlabel('Wavenumber (10^3 cm^{-1})')
ylabel('Absorption (a.u.)')

ax2 = axes(t);
plot(ax2, wavelength, data, '-g')
ax2.XAxisLocation = 'top';
xlabel('Wavelength (nm)')

[Cris LaPierre]

First, your second axes is covering the first one. You need to turn the background off.

Otherwise, this is the same issue as OP. The difference between each wavelength is the same: 1. The difference between each wavenumber is not the same.

wavelength = 300:1600; % in nm
wavenumber = 1e7./wavelength; % in cm-1
data = rand(1, length(wavenumber));

figure
plot(diff(wavelength))
hold on
plot(diff(wavenumber))
hold off

Therefore, when you plot the two on the same axis, the two signals will not align.

figure
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1, wavenumber(1:20), data(1:20), '-b')
set(gca, 'XDir','reverse')
xlim(wavenumber([20 1]))

ax2 = axes(t);
plot(ax2, wavelength(1:20), data(1:20), '--r')
ax2.XAxisLocation = 'top';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlim(wavelength([1 20]))

As with the OP, you need to plot both signals using the same X values, and then convert the ticks of one to the other scale.

You can do that using wavenumber:

figure
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1, wavenumber/1e3, data, '-r')
set(ax1, 'XDir','reverse')
xlabel('Wavenumber (10^3 cm^{-1})')
ylabel('Absorption (a.u.)')

ax2 = axes(t);
plot(ax2, wavenumber/1e3, data, '--g')
set(ax2, 'XDir','reverse')
ax2.XAxisLocation = 'top';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlabel('Wavelength (nm)')

% desired wavelength tick locations
wvlgth = [1600 1000 800 600 500 400 300];

% corresponding wavenumber in cm^-1
wvlg_nmTk = 1e7./wvlgth/1e3

wvlg_nmTk = 1×7

6.2500 10.0000 12.5000 16.6667 20.0000 25.0000 33.3333

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xticks(ax2,wvlg_nmTk);
xticklabels(ax2,sprintf('%3.0f\n',wvlgth)); % display in meters

or wavelength:

Note how the plot looks different depending which one you use because of the difference in step (constant vs changing).

figure
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1, wavelength, data, '-r')
xlabel('Wavenumber (10^3 cm^{-1})')
ylabel('Absorption (a.u.)')

ax2 = axes(t);
plot(ax2, wavelength, data, '--g')
ax2.XAxisLocation = 'top';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlabel('Wavelength (nm)')

% desired wavelength tick locations
wvnum = [35 25 20 15 12 10 8 7]; % 1e3 cm^-1
wvnum = wvnum*1e3; % cm^-1

% corresponding wavelength in nm
wvlg_nmTk = 1e7./wvnum

wvlg_nmTk = 1×8

1.0e+03 * 0.2857 0.4000 0.5000 0.6667 0.8333 1.0000 1.2500 1.4286

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xticks(ax1,wvlg_nmTk);
xticklabels(ax1,sprintf('%3.0f\n',wvnum/1e3)); % display in 1e3 cm^-1

[Anna]

Hi Cris, thank you so much. This code has been very helpful. I am just wondering how to adjust the x-axis limits. For example, I want to set the wavelength range from 400 to 1400 nm. Unfortunately, using xlim(ax2, [400 1400]) results in disappearing of the data from the top axis. Thank you! :)

[Cris LaPierre]

Please share a working example. Adding that to the code above does not remove anything from the plot.

However, at least in the OP, the intent was to align the top and bottom axes. Setting the limits of one axis without adjusting the other would possibly lead to misinterpretation of the data since wavenumber and wavelength are related.

wavelength = 300:1600; % in nm
wavenumber = 1e7./wavelength; % in cm-1
data = rand(1, length(wavenumber));

figure
t = tiledlayout(1,1);
ax1 = axes(t);
plot(ax1, wavelength, data, '-r')
xlabel('Wavenumber (10^3 cm^{-1})')
ylabel('Absorption (a.u.)')

ax2 = axes(t);
plot(ax2, wavelength, data, '--g')
ax2.XAxisLocation = 'top';
ax2.Color = 'none';
ax1.Box = 'off';
ax2.Box = 'off';
xlabel('Wavelength (nm)')

% desired wavelength tick locations
wvnum = [35 25 20 15 12 10 8 7]; % 1e3 cm^-1
wvnum = wvnum*1e3; % cm^-1

% corresponding wavelength in nm
wvlg_nmTk = 1e7./wvnum

wvlg_nmTk = 1×8

1.0e+03 * 0.2857 0.4000 0.5000 0.6667 0.8333 1.0000 1.2500 1.4286

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xticks(ax1,wvlg_nmTk);
xticklabels(ax1,sprintf('%3.0f\n',wvnum/1e3)); % display in 1e3 cm^-1

xlim(ax2, [400 1400])