dipolarkernel

Computes the dipolar kernel matrix that transforms a distance distribution to a time-domain dipolar signal.

Syntax

K = dipolarkernel(t,r)
K = dipolarkernel(t,r,lambda)
K = dipolarkernel(t,r,pathinfo)
K = dipolarkernel(t,r,lambda,B)
K = dipolarkernel(t,r,pathinfo,B)
K = dipolarkernel(___,'Property',Value)
Parameters
  • t - Time axis vector (N-element array), in microseconds
  • r - Distance axis vector (M-element array), in nanometers
  • lambda - Modulation depth (scalar)
  • pathinfo - Modulation depths, refocusing times, and harmonics (px2 or px3 array) for multiple dipolar pathways
  • B - Background, either vector of values (N-element array) or function handle
Returns
  • K - Dipolar kernel matrix (NxM array)

Description

K = dipolarkernel(t,r)

Computes the elementary kernel matrix K for the time axis t (in microseconds) and distance axis r (in nanometers).The dipolar kernel is normalized by \Delta r, such that it returns a dipolar signal with amplitude 1 at time zero for a normalized distance distribution (i.e. trapz(r,P)==1).

K = dipolarkernel(t,r,lambda)

If the modulation depth lambda (a number between 0 and 1) is specified, then it is included into the kernel matrix.

K = dipolarkernel(t,r,lambda,B)

If the background B and modulation depth lambda are specified, then both are included into the kernel matrix. B can be either an array with the pre-calculated background decay (over t), or a function handle with a background model.

K = dipolarkernel(t,r,pathinfo)
K = dipolarkernel(t,r,pathinfo,B)

For a multi-pathway DEER signal (e.g, 4-pulse DEER with 2+1 contribution; 5-pulse DEER with 4-pulse DEER residual signal, and more complicated experiments), pathinfo is a 2D array that contains a list of modulation depths (amplitudes), refocusing times (in microseconds), and optional harmonics for all modulated pathway signals.

Each row of pathinfo contains two values: one modulation depth and one refocusing time. For a pathway with unmodulated signal, set the refocusing time to NaN.

Optionally, the harmonic (1 = fundamental, 2 = first overtone, etc.) can be given as a third value in each row. This can be useful for modeling RIDME signals. If not given, the harmonic is 1 for all pathways.

In these cases, the background model must be specified as a function handle accepting the time-axis t and pathway amplitude lambda as inputs, i.e. B = @(t,lambda) bg_model(t,param,lambda).

Example 1:
To specify the standard model for 4-pulse DEER with an unmodulated offset and a single dipolar pathway that refocuses at time 0, use
lambda = 0.4; % modulation depth main signal

pathinfo = [1-lambda NaN; lambda 0];

% alternative input
pathinfo(1,:) = [1-lambda NaN];    % unmodulated part, gives offset
pathinfo(2,:) = [lambda 0];        % main modulation, refocusing at time zero

K = dipolarkernel(t,r,pathinfo);

The shorthand input syntax dipolarkernel(t,r,lambda) is equivalent to this input.

Example 2:
To specify a more complete 4-pulse DEER model that includes the 2+1 contribution, use
Lambda0 = 0.5;   % unmodulated part
lambda = 0.4;    % modulation depth main signal
lambda21 = 0.1;  % modulation depth 2+1 contribution
tau2 = 4;        % refocusing time of 2+1 contribution

pathinfo(1,:) = [Lambda0  NaN];     % unmodulated part, gives offset
pathinfo(2,:) = [lambda4  0];       % main modulation, refocusing at time zero
pathinfo(2,:) = [lambda21 tau2];    % 2+1 modulation, refocusing at time tau2

K = dipolarkernel(t,r,pathinfo);

Additional Settings

Additional settings can be specified via name-value pairs. All property names are case insensitive and the property-value pairs can be passed in any order after the required input arguments have been passed.

K = dipolarkernel(___,'Property1',Value1,'Property2',Value2,___)
  • 'ExcitationBandwidth' - Excitation bandwidth of the pulses in MHz.

    Use this to include limited excitation bandwidth of the experimental pulses. If not specified, infinite excitation bandwidth is assumed.

    Default: [empty]

    Example:

    K = dipolarkernel(___,'ExcitationBandwidth',50)     % 50 MHz excitation bandwidth
  • 'OvertoneCoeffs' - RIDME overtone coefficients

    1D array containing the overtone coefficients for RIDME experiments. If passed, the dipolar kernel overtones are calculated based on the passed coefficients.

    Default: [empty]

    Example:

    K = dipolarkernel(___,'OvertoneCoeffs',[0.4 0.2 0.4])   % fundamental, 1st, and 2nd overtone
  • 'g' - Electron g-value

    Specifies the two g-values of the electron spin centers used to compute the dipolar frequencies from the given distance axis.

    Default: free-electron g value

    Example:

    K = dipolarkernel(___,'g',[2.01 2.1])
  • 'Method' - Kernel matrix calculation method

    Specifies the method the kernel matrix is computed numerically.

    • 'fresnel' - Uses Fresnel integrals. This method is fast and accurate.
    • 'integral' - Uses MATLAB’s integral() function. This method is accurate, but slow.
    • 'grid' - Uses orientation averaging over a grid of orientations, using the number of orientations given in nKnots. This method is slow, and it converges very slowly with the number of orientations.

    Default: 'fresnel'

    Example:

    K = dipolarkernel(___,'Method','integral')
  • 'nKnots' - Number of orientations for orientation averaging

    If the kernel is computed using 'grid', this options specifies the number of orientations between \theta=0 and \theta=\pi/2 used for orientation averaging.

    Default: 5001

    Example:

    K = dipolarkernel(___,'Method','grid','nKnots',1e4)
  • 'Renormalize' - Re-normalization of multi-pathway dipolar kernels

    If the kernel is computed for a multi-pathway model via the pathinfo variable, the kernel does not necessarily satisfy V(0) == 1. This option enables(true) or disables(false) a re-normalization to ensure that equality is satisfied.

    Default: true

    Example:

    K = dipolarkernel(___,'Renormalize',false)