HKL_signal (160901, 170113)

hkl_signal <HKL project> <resolution>

This command allows you to visualise the signal (defined for each reflection as the ratio of the experimental structure factor intensity and the equivalent standard deviation, I/Sig(I)) in an HKL project that has already been loaded into the O session with the HKL_read command. The command is also accessible from the pull-down Rebuild menu system via the the ‘*** HKL signal ***’ blind, which is described in more detail below.

HKL_signal generates a number of 3D objects, as well as text in the terminal window that includes a detailed description of relevant signal statistics. All objects are centred at (0,0,0) in space.


3D objects created by HKL_signal

LATTICE is a 3D representation of the reciprocal lattice. Each reflection in the HKL project is colour coded according to the signal in the usual blue-red rainbow scheme and expanded as appropriate for the space group symmetry to generate a complete sphere of data. Depending on the setting of an ODB entry (see below), either all reflections within the resolution limit or those in the three principal planes of the lattice are drawn (each as a small 3D cross). The object generated for the complete reciprocal lattice, therefore, provides a detailed, per reflection view of the signal over all measurements, but is somewhat overwhelming in size and complexity.


Complete reciprocal lattice for a 1.4 Å resolution PfDXR-inhibitor complex. Note the PAC-MAN-like jaws that correspond to regions of missing reflections along the spindle axis of the diffractometer.


The principal planes of the reciprocal lattice for a 1.4 Å resolution PfDXR-inhibitor complex. Note the PAC-MAN-like jaws that correspond to regions of missing reflections along the spindle axis of the diffractometer, are no longer so obvious.


Zooming in on the above object shows each reflection as a coloured, small, 3D cross.

The RECELL object is a representation of the reciprocal lattice vectors with resolution ticks along each axis.


SIGNAL is a FastMap object that has been generated from the locally averaged signal in the full reciprocal lattice. As such, the SIGNAL map can be contoured at any value of the signal (I/sig(I)), or indeed at multiple levels. The brick size and averaging radius are defined in the ODB, which is described in more detail below.



The above two figures show the SIGNAL map contoured at an I/sig(I) value of 2.0 (one image has been clipped to show the missing cone of diffraction data). Note that despite the averaging of the signal, the outer surface remains somewhat rough.


Contouring at a signal level of 8.0 reduces the volume of reciprocal lattice that is contained within the contours. The missing cone regions are still visible to the left and right

The user is already able to see in this example that the intensity distribution is not isotropic as a function of the resolution. To quantitatively define the anisotropy, an inertia matrix is calculated from the signal map, and its Eigen values and vectors are calculated. The orthogonal Eigen vector directions are drawn in the EIGVEC object such that the red line indicates the direction with the most rapid fall-off of signal, the green line the direction of the second fastest fall-off, and blue defines the direction of the slowest fall-off.

The signal has been contoured at 3.5 in the next series of images and the difference in resolution drop-off along the 3 orthogonal directions is clearly indicated along the Eigen vector directions.


The view has been chosen to show the most rapid drop-off in the signal in the vertical direction, and the slowest drop-off along the horizontal .


Close up of the most rapid signal fall-off, along the RED Eigen vector 


The signal fall-off in the direction of the GREEN Eigen vector is clearly less than along the RED direction.


The signal along the BLUE Eigen vector extends to the highest resolution but also abuts the missing cone of un-recorded reflection data.

The fifth object PRNCPL draws the reciprocal lattice points that exist within cylindrical volumes along  the Eigen vectors. This object, together with the EIGVEC and SIGNAL objects, allow the user to understand how the diffraction data is affected by anisotropy and to decide on the resolution along the appropriate directions for the desired signal in the measurements.


The change in colour along the cylindrical volumes clearly indicate the anisotropic nature of the diffraction data.

Once the user has decided on the appropriate signal, the most accurate resolution for the data along each Eigen vector can be determined by inspecting the output directed to the terminal. The signal is first evaluated in 20 thin spherical shells, and then in 20 cylindrical shells along the Eigen vectors:

 O > HKL_signal

 New> What hkl project? [NATI]:

 New> Resolution [ 1.40]:


 New> This command makes a number of 3D objects:

 New> Lattice - a 3D reciprocal lattice, colour code by signal.

 New> Recell - the reciprocal cell axes with resolution ticks.

 New> Signal - a FastMap of the locally averaged signal.

 New> Eigvec - the Eigen vectors of the mass weighted signal map.

 New> Prncpl - colour coded average signal in cylinders along the Eigen vectors.

 New> Signal map brick size is  0.040

 New> Radius for averaging signal is  0.050

 New> Render space full

 New> No can chip


 New> Signal in spherical resolution shells.

 New> Resolution    Signal    Reflections

 New>      28.00     19.62        30

 New>      14.00     25.41       312

 New>       9.33     35.70       848

 New>       7.00     29.95      1628

 New>       5.60     24.75      2730

 New>       4.67     28.75      4018

 New>       4.00     28.65      5618

 New>       3.50     26.05      7434

 New>       3.11     20.69      9630

 New>       2.80     17.71     11926

 New>       2.55     14.85     14492

 New>       2.33     12.86     17394

 New>       2.15     11.31     20464

 New>       2.00      8.49     23788

 New>       1.87      6.15     27346

 New>       1.75      4.37     31144

 New>       1.65      3.34     35144

 New>       1.56      2.62     39370

 New>       1.47      2.01     43704

 New>       1.40      1.56     48490

 New> Overall average I/sig(I) 7.51, for 345510 reflections.


 New> Signal 3D shape evaluation.

 New> Eigen values:      1.12      1.06      1.00

 New> Eigen vectors (most anisotropic direction first).

 New> Eigen vector:    0.2948    0.7768   -0.5565

 New> Eigen vector:    0.2787    0.4871    0.8277

 New> Eigen vector:    0.9140   -0.3991   -0.0729


 New> Signal along Eigen vectors (most anisotropic first).

 New> Eigen Vector number     1

 New> Resolution    Signal    Reflections

 New>      28.00     23.72       258

 New>      14.00     32.09       270

 New>       9.33     35.70       266

 New>       7.00     28.45       264

 New>       5.60     25.76       272

 New>       4.67     29.44       268

 New>       4.00     24.42       266

 New>       3.50     23.94       260

 New>       3.11     16.18       274

 New>       2.80     16.26       266

 New>       2.55     12.65       272

 New>       2.33     11.74       262

 New>       2.15      9.23       268

 New>       2.00      6.00       264

 New>       1.87      3.75       278

 New>       1.75      3.00       264

 New>       1.65      1.83       272

 New>       1.56      1.55       266

 New>       1.47      1.34       272

 New>       1.40      1.12       256

 New> Overall average I/sig(I) 15.39, for 5338 reflections.


 New> Eigen Vector number     2

 New> Resolution    Signal    Reflections

 New>      28.00     25.65       256

 New>      14.00     30.70       262

 New>       9.33     37.21       268

 New>       7.00     26.06       268

 New>       5.60     21.90       268

 New>       4.67     27.42       270

 New>       4.00     25.92       274

 New>       3.50     24.53       272

 New>       3.11     17.41       264

 New>       2.80     17.64       266

 New>       2.55     14.92       260

 New>       2.33     12.67       276

 New>       2.15     10.15       258

 New>       2.00      7.95       276

 New>       1.87      5.56       264

 New>       1.75      3.80       262

 New>       1.65      4.00       266

 New>       1.56      2.95       272

 New>       1.47      2.37       274

 New>       1.40      1.74       258

 New> Overall average I/sig(I) 16.03, for 5334 reflections.


 New> Eigen Vector number     3

 New> Resolution    Signal    Reflections

 New>      28.00     27.26       266

 New>      14.00     29.61       258

 New>       9.33     32.24       260

 New>       7.00     26.01       258

 New>       5.60     26.26       256

 New>       4.67     29.92       252

 New>       4.00     30.79       250

 New>       3.50     31.94       250

 New>       3.11     25.88       258

 New>       2.80     22.49       260

 New>       2.55     17.76       258

 New>       2.33     16.91       256

 New>       2.15     16.90       258

 New>       2.00     12.60       248

 New>       1.87     10.01       250

 New>       1.75      9.11       248

 New>       1.65      5.42       232

 New>       1.56      5.07       210

 New>       1.47      4.07       194

 New>       1.40      2.69       178

 New> Overall average I/sig(I) 19.84, for 4900 reflections.


We can, therefore, quote the signal in the outer 1.4 Å resolution spherical shell as 1.56 or we could quote a resolutions at which we have a particular signal; a ‘2 sigma signal’, for example, is obtained at 1.47 Å resolution. However, a more accurate picture that takes into account the anisotropy of the measurements would define the signal in the highest resolution cylindrical shell along each Eigen vector as (1.12, 1.74, 2.69), or we could quote resolutions of (1.66, 1.43, 1.40) Å for the 2 sigma signal.

HKL_signal makes use of default values that are stored in the user’s O data-base in the integer vector .hkl_aniso with the following default values

 O > writ .hkl_aniso ;;

.HKL_ANISO                I          4 (16(1x,i4))                             

    0 2000    4    5

The first entry determines if the full lattice (value 0), or if 3 sets of principal zones (value 1) is to be drawn.

The second item determines how a reciprocal space distance is mapped into the real space of O and is scaled internally by dividing by 100.

The third item determines the SIGNAL brick size in reciprocal Ångström units and is scaled internally by dividing by 100.

The fourth item determines the averaging radius around each point in the SIGNAL map that is used to generate the signal, in reciprocal Ångström units, and is scaled internally by dividing by 100.

Default values are set if the entry does not exist.

A user may prefer to access this option via the Master Menu Rebuild Interface from the ‘** HKL signal **’ blind. Clicking on this text expands or contracts the blind. 


The expanded blind allows the user to draw a complete set of 3D lattice points, or the 3 principal planes of data. Clicking on either, generates a popup menu to activate the command. The colours indicate the rainbow ramping used to generate the lattice points; blue indicates a very strong signal while red lattice points have a very low signal.