XSLT numerical search of z-filter ±3QMAS cogwheel phase cycling parameters

In phase-modulated three-pulse split-t1 MQMAS sequence, one coherence transfer pathway is involved. Now, we extend our method to amplitude-modulated three-pulse z-filter ±3QMAS sequence applied to a spin I = 3/2 system. Two symmetrical coherence transfer pathways are involved.

In the XML modelling steps for split-t1 sequence, we have generated an mqmas.xml file on WINDOWS desktop. It remains valid for z-filter sequence with minor modification (see below). Now we associate a modified XSLT (eXtensible Stylesheet Language Transformation) file still called mqmas.xsl with the mqmas.xml file to search the winding numbers satisfying two conditions, one for the antiecho coherence transfer pathway and another one for the echo coherence transfer pathway:

It is equivalent to the two conditions:

Hughes and coworkers provide us with formulae for estimating the number N of steps in the phase cycling. In this case N = 24.

For spin I = 3/2 system, the antiecho coherence transfer pathway 0Q -> 3Q -> 0Q -> -1Q is decribed by $p_{\mathrm{AB}}^0$ = 3 and $p_{\mathrm{BC}}^0$ = 0. The echo coherence transfer pathway 0Q -> -3Q -> 0Q -> -1Q is decribed by $p_{\mathrm{AB}}^1$ = -3 and $p_{\mathrm{BC}}^1$ = 0.

It is well known from nested phase cycling procedure that one of the pulse phases can be zero. We choose to set the winding number of the first pulse to zero, $w_A$ = 0.

Step 1: Generate mqmas.xml on WINDOWS desktop

First download the Java file called XmlData.java. Then replace the following two lines:

      int windingB = 23;                //winding number wB of the 2nd-pulse B
      int windingC = 23;                //winding number wC of the 3rd-pulse C
    

      int windingB = 24;                //winding number wB of the 2nd-pulse B
      int windingC = 24;                //winding number wC of the 3rd-pulse C
    

Finally, generate the mqmas.xml file as shown in XML modelling of MQMAS sequence web page.

Step 2: Download mqmas.xsl on WINDOWS desktop

By downloading mqmas.xsl, we have two files on WINDOWS desktop: mqmas.xml and mqmas.xsl, check their file extensions.

Step 3: Modify mqmas.xsl

Replace the condition involved in phase-modulated split-t1 sequence:

      <xsl:template match="C[((../@w - ../../@w)*(../../@p - 3) 
                     + (@w - ../@w)*(../@p - 1)) mod 23 = 0]">
    

      <xsl:template match="C[((../@w - ../../@w)*(../../@p - 3) 
                     + (@w - ../@w)*(../@p - 0)) mod 24 = 0 and 
                             ((../@w - ../../@w)*(../../@p + 3) 
                     + (@w - ../@w)*(../@p + 0)) mod 24 = 0]">
    

Step 4: Numerical search

By clicking the mqmas.xml file icon on WINDOWS desktop with the mouse, the default web browser starts. Then it presents a 5-column table. In order to save this table for further analyses, first we select and copy the web page, then paste the data in an MS EXCEL spreadsheet called initial.