slmsuite.holography.algorithms.Hologram

class Hologram(target, amp=None, phase=None, slm_shape=None, dtype=<class 'numpy.float32'>, propagation_kernel=None, **kwargs)

Bases: Hologram

Phase retrieval methods applied to holography (DFT-based). See optimize() to learn about the methods implemented for hologram optimization.

Tip

The Fourier domain ("kxy") of an SLM with shape slm_shape also has the shape slm_shape under discrete Fourier transform. The extents of this domain correspond to the edges of the farfield determined by physical constants as \(\pm\frac{\lambda}{2\Delta x}\) radians, where \(\Delta x\) is the SLM pixel pitch. This means that resolution of the farfield \(\pm\frac{\lambda}{2N_x\Delta x}\) radians can be quite poor with small resolution \(N_x\). The solution is to zero-pad the SLM nearfield — artificially increasing the width \(N_x\) and height \(N_y\) while the extent of the non-zero nearfield data remains the same — and thus enhance the resolution of the farfield. In practice, padding is accomplished by passing a shape or target of appropriate shape (see constructor __init__() and subclasses), potentially with the aid of the static helper function get_padded_shape().

Note

target, weights, phase_ff, and amp_ff are all matrices of shape shape. To save memory, the matrices phase and amp are stored with the (smaller, but not strictly smaller) shape slm_shape. Also to save memory, phase_ff and amp_ff are set to None on construction, and only initialized if they need to be used. Any code additions should check for None.

Tip

Due to imperfect SLM diffraction efficiency, undiffracted light will be present at the center of the target. This is called the zeroth order diffraction peak. To avoid this peak, consider shifting the data contained in target away from the center.

Tip

For mixed region amplitude freedom (MRAF) capabilities, set the part of the target desired as a ‘noise region’ to nan. See optimize() for more details. SpotHologram has spot-specific methods for generated noise region pattern.

Caution

By default, arguments passed to the constructor (phase, amp, … ) are stored directly as attributes without copying, when possible. These will be modified in place. However, numpy arrays passed to cupy will naturally be copied onto the GPU and arrays of incorrect dtype will likewise be copied and casted. This lack of copying is desired in many cases, such that external routines access the same data, but the user can choose to pass copied arrays if this behavior is undesired.

slm_shape

The shape of the nearfield device producing the hologram in the farfield in numpy (h, w) form. This is important to record because certain optimizations and calibrations depend on it. If multiple of slm_shape, phase, or amp are not None in the constructor, the shapes must agree. If all are None, then the shape of the target is used instead (slm_shape == shape).

Type:

(int, int)

shape

The shape of the computational space in the nearfield and farfield in numpy (h, w) form. Corresponds to the the "knm" basis in the farfield. This often differs from slm_shape due to padding of the nearfield.

Type:

(int, int)

phase

nearfield phase pattern to optimize. Initialized to with random.default_rng().uniform() by default (None). This is of shape slm_shape and (upon copying to nearfield during optimization) padded to shape shape.

Type:

numpy.ndarray OR cupy.ndarray

amp

nearfield source amplitude pattern (i.e. image-space constraints). Uniform illumination is assumed by default (None). This is of shape slm_shape and (upon copying to nearfield during optimization) padded to shape shape.

Type:

numpy.ndarray OR cupy.ndarray

nearfield

Helper variable to encode the data in phase and amp as a single complex matrix. This is of shape shape.

Type:

numpy.ndarray OR cupy.ndarray

target

Desired farfield amplitude in the "knm" basis. The goal of optimization. This is of shape shape in DFT-based algorithms, but differs for CompressedSpotHologram.

Type:

numpy.ndarray OR cupy.ndarray

weights

The mutable farfield amplitude in the "knm" basis used in GS. Starts as target but may be modified by weighted feedback in WGS. This is of the same shape as target.

Type:

numpy.ndarray OR cupy.ndarray

farfield

Helper variable to encode the data in the farfield as a single complex matrix. This is of the same shape as target.

Type:

numpy.ndarray OR cupy.ndarray

phase_ff

Algorithm-constrained farfield phase in the "knm" basis. Used as a helper variable for optimization. Stored for computational algorithms which desire to fix the phase in the farfield (see optimize_gs()). This is of the same shape as target.

Type:

numpy.ndarray OR cupy.ndarray

amp_ff

Farfield amplitude in the "knm" basis. Used for comparing this, the computational result, with the target. This is of the same shape as target.

Type:

numpy.ndarray OR cupy.ndarray OR None

dtype

Datatype for real arrays. The default is float32.

Type:

type

dtype_complex

Datatype for complex arrays. The complex numbers follow numpy type promotion. Complex datatypes are derived from dtype:

• float32 -> complex64 (the default dtype)

• float64 -> complex128

float16 is not recommended for dtype because complex32 is not implemented by numpy.

Type:

type

propagation_kernel

Allows the user to target holography at different depths or aberration spaces. This is also applied for FeedbackHologram and subclasses to ~slmsuite.holography.algorithms.FeedbackHologram.measure() the hologram at the desired plane. If None, this feature is not used and no depth or aberration transformation is applied.

Type:

numpy.ndarray OR cupy.ndarray OR None

iter

Tracks the current iteration number.

Type:

int

flags

Helper flags to store custom persistent variables for optimization. These flags are generally changed by passing as a kwarg to optimize(). Contains the following keys:

• "method"str

  Stores the method used for optimization. See optimize().

• "fixed_phase"bool

  Fixes the farfield phase as mandated by certain weighted algorithms (see optimize_gs()).

• "feedback"str

  Stores the values passed to optimize().

• "stat_groups"list of str

  Stores the values passed to optimize().

• "raw_stats"bool

  Whether to store raw stats: the raw image and feedback data for each iteration. Note that this can be a good amount of data.

• "blur_ij"float

  See ijcam_to_knmslm().

• Other user-defined flags.

Type:

dict

stats

Dictionary of useful statistics. data is stored in lists, with indices corresponding to each iteration. Contains:

• "methods"list of str

  Method used for each iteration.

• "flags"dict of lists

  Each key corresponds to a flag that was used at least once. If it is np.nan on a given iteration, then it was undefined at that point (update functions keep track of all this).

• "stats"dict of dicts of lists

  Same format as "flags", except with another layer of hierarchy corresponding to the source (group) of the given stats. This is to differentiate standard deviations computed computationally and experimentally.

See _update_stats() and plot_stats().

Type:

dict

Methods

get_farfield	Collects the current complex DFT farfield, potentially with transformations.
get_mempool_limit	Helper function to get the cupy memory pool size.
get_padded_shape	Helper function to calculate the shape of the computational space.
get_phase	Collects the current nearfield phase from the GPU with cupy.ndarray.get().
load_stats	Uses save_h5() to import the statistics hierarchy from a given h5 file.
optimize	Optimizers to solve the "phase problem": approximating the nearfield phase that transforms a known nearfield source amplitude to a desired farfield target amplitude.
optimize_cg	Conjugate Gradient (CG) iterative phase retrieval.
optimize_gs	GPU-accelerated Gerchberg-Saxton (GS) iterative phase retrieval.
plot_farfield	Plots an overview (left) and zoom (right) view of source.
plot_nearfield	Plots the amplitude (left) and phase (right) of the nearfield (plane of the SLM).
plot_stats	Plots the statistics contained in the given dictionary.
remove_vortices	Removes the computed phase vortices in the farfield where the target amplitude is positive.
reset	Resets the hologram to an initial state.
reset_phase	Resets the hologram to a provided phase, to a random state, or to a quadratic phase which overlaps with the target pattern.
reset_weights	Resets the hologram weights to the target defaults.
save_stats	Uses save_h5() to export the statistics hierarchy to a given h5 file.
set_mempool_limit
set_target	Change the target to something new.

__init__(target, amp=None, phase=None, slm_shape=None, dtype=<class 'numpy.float32'>, propagation_kernel=None, **kwargs)

Initialize datastructures for optimization. When cupy is enabled, arrays are initialized on the GPU as cupy arrays: take care to use class methods to access these parameters instead of editing them directly, as cupy arrays behave slightly differently than numpy arrays in some cases.

Parameters additional to class attributes are described below:

Parameters:

• target (numpy.ndarray OR cupy.ndarray OR (int, int) OR None) – Target to optimize to. The user can also pass a shape in numpy (h, w) form, and this constructor will create an empty target of all zeros. get_padded_shape() can be of particular help for calculating the shape that will produce desired results (in terms of precision, etc). None is used internally.

• amp (array_like OR None) – The nearfield amplitude. See amp. Of shape slm_shape.

• phase (array_like OR None) – The nearfield initial phase. See phase. phase should only be passed if the user wants to precondition the optimization. Of shape slm_shape.

• slm_shape ((int, int) OR slmsuite.hardware.FourierSLM OR slmsuite.hardware.slms.SLM OR None) – The shape of the nearfield of the SLM in numpy (h, w) form. Optionally, as a quality of life feature, the user can pass a FourierSLM or SLM instead, and slm_shape (and amp if it is None) are populated from this. If None, tries to use the shape of amp or phase, but if these are not present, defaults to shape (which is usually determined by target).

• dtype (type) – See dtype; the type to use for stored arrays. The user should choose this as a tradeoff between precision, memory size, and compute time.

• propagation_kernel (array_like OR None) –

  Primarily used for targeting holography at a different depth plane, encoded by a focusing kernel. MultiplaneHologram, targeting several depth planes, must make use of this parameter to ‘bake’ the information for each plane into the composite hologram. A more advanced use of this feature is to target different positions in aberration-space, i.e. have a unique wavefront calibration baked into the hologram for each plane.

  The kernel must be of shape slm_shape. If None, this feature is unused (the kernel is an ideal DFT).

  Tip

  The unit conversions necessary to convert a depth into a Zernike focusing parameter are stored in a cameraslm, and can be accessed via convert_vector().

  # Convert a floating point Z depth from a desired units to Zernike units.
  depth_zernike = convert_vector(
      (0, 0, depth),
      from_units="{depth_units}",
      to_units="zernike",
      hardware=cameraslm,
  )
  
  # The ANSI Zernike indices (2,1,4) [x,y,z]
  # are automatically assumed from the 3-vector.
  propagation_kernel = toolbox.phase.zernike_sum(
      grid=cameraslm,
      weights=depth_zernike,
  )
  

  Note

  Is ignored for CompressedSpotHologram.

• **kwargs – Passed to flags.

get_farfield(shape=None, propagation_kernel=None, affine=None, get=True)

Collects the current complex DFT farfield, potentially with transformations. This includes collecting the data from the GPU with cupy.ndarray.get().

Parameters:

• shape ((int, int)) – Shape of the DFT. Useful to change the resolution of the farfield. If None, defaults to shape, and falls back to slm_shape.

• propagation_kernel (array_like) – Used to check the result of the hologram at different depths. See propagation_kernel. If None, defaults to propagation_kernel if one is present. Otherwise, no kernel is applied. Zeroing can force no kernel to be applied and yield the raw DFT.

• affine (dict) – Affine transformation to apply to farfield data (in the form of a dictionary with keys "M" and "b"). If None, no transformation is applied.

• get (bool) – Whether or not to convert the cupy array to a numpy array if cupy is used. This is ignored if numpy is used.

Returns:

Current farfield expected from the current phase.

Return type:

numpy.ndarray

static get_mempool_limit(device=0)

Helper function to get the cupy memory pool size.

Parameters:

device (int) – Which GPU to set the limit on. Passed to cupy.cuda.Device().

Returns:

Current memory pool limit in bytes

Return type:

int

static get_padded_shape(slm_shape, padding_order=1, square_padding=True, precision=inf, precision_basis='kxy')

Helper function to calculate the shape of the computational space. For a given base slm_shape, pads to the user’s requirements. If the user chooses multiple requirements, the largest dimensions for the shape are selected. By default, pads to the smallest square power of two that encapsulates the original slm_shape.

See also

Hologram

Note

Under development: a parameter to pad based on available memory (see _calculate_memory_constrained_shape()).

Parameters:

• slm_shape ((int, int) OR slmsuite.hardware.FourierSLM) – The original shape of the SLM in numpy (h, w) form. The user can pass a FourierSLM or SLM instead, and should pass this when using the precision parameter.

• padding_order (int) – Scales to the padding_order th larger power of 2. A padding_order of zero does nothing. For instance, an SLM with shape (720, 1280) would yield (720, 1280) for padding_order=0, (1024, 2048) for padding_order=1, and (2048, 4096) for padding_order=2.

• square_padding (bool) – If True, sets the smaller shape dimension to that of the larger, yielding a square.

• precision (float) – Returns the shape that produces a computational k-space with resolution smaller than precision. The default, infinity, requests a padded shape larger than zero, so padding_order will dominate.

• precision_basis (str) – Basis for the precision. Can be "ij" (camera) or "kxy" (normalized blaze).

Returns:

Shape of the computational space which satisfies the above requirements.

Return type:

(int, int)

get_phase(include_propagation=False)

Collects the current nearfield phase from the GPU with cupy.ndarray.get(). Also shifts the \([-\pi, \pi]\) range of numpy.arctan2() to \([0, 2\pi]\) for faster writing to the SLM (see set_phase()).

Parameters:

include_propagation (bool) – Whether to include the propagation_kernel, if available.

Returns:

Current nearfield phase of the optimization.

Return type:

numpy.ndarray

load_stats(file_path, include_state=True)

Uses save_h5() to import the statistics hierarchy from a given h5 file.

Tip

Enabling the "raw_stats" flag will export feedback data from each iteration instead of only derived statistics. Consider enabling this to save more detailed information upon export.

Parameters:

• file_path (str) – Full path to the file to read the data from.

• include_state (bool) – If True, also overwrite all other attributes of Hologram except for dtype and amp_ff.

optimize(method='GS', maxiter=20, verbose=True, callback=None, feedback=None, stat_groups=[], **kwargs)

Optimizers to solve the “phase problem”: approximating the nearfield phase that transforms a known nearfield source amplitude to a desired farfield target amplitude. Supported optimization methods include:

• Gerchberg-Saxton (GS) phase retrieval.

  • 'GS'

    An iterative algorithm for phase retrieval, accomplished by moving back and forth between the imaging and Fourier domains, with amplitude corrections applied to each. This is usually implemented using fast discrete Fourier transforms, potentially GPU-accelerated.

• Weighted Gerchberg-Saxton (WGS) phase retrieval algorithms of various flavors. Improves the uniformity of GS-computed focus arrays using weighting methods and techniques from literature. The method keywords are:

  • 'WGS-Leonardo'

    The original WGS algorithm. Weights the target amplitudes by the ratio of mean amplitude to computed amplitude, which amplifies weak spots while attenuating strong spots. Uses the following weighting function:

    \[\mathcal{W} = \mathcal{W}\left(\frac{\mathcal{T}}{\mathcal{F}}\right)^p\]

    where \(\mathcal{W}\), \(\mathcal{T}\), and \(\mathcal{F}\) are the weight amplitudes, target (goal) amplitudes, and feedback (measured) amplitudes, and \(p\) is the power passed as "feedback_exponent" in flags (see kwargs). The power \(p\) defaults to .8 if not passed. In general, smaller \(p\) will lead to slower yet more stable optimization.

  • 'WGS-Kim'

    Improves the convergence of WGS-Leonardo by fixing the farfield phase strictly after a desired number of net iterations specified by "fix_phase_iteration" or after exceeding a desired efficiency (fraction of farfield energy at the desired points) specified by "fix_phase_efficiency"

  • 'WGS-Nogrette'

    Weights target intensities by a tunable gain factor.

    \[\mathcal{W} = \mathcal{W}/\left(1 - f\left(1 - \mathcal{F}/\mathcal{T}\right)\right)\]

    where \(f\) is the gain factor passed as "feedback_factor" in flags (see kwargs). The factor \(f\) defaults to .1 if not passed.

    Note that while Nogrette et al compares powers, this implementation compares amplitudes for speed. These are identical to first order.

  • 'WGS-Wu'

    Weights using an exponential function, which is less sensitive to near-zero values of \(\mathcal{F}\) or \(\mathcal{T}\).

    \[\mathcal{W} = \mathcal{W}\exp\left( p (\mathcal{T} - \mathcal{F}) \right)\]

    The speed of correction is controlled by \(p\), the power passed as "feedback_exponent".

  • 'WGS-tanh'

    Weights by hyperbolic tangent, commonly used as an activation function in machine learning.

    \[\mathcal{W} = \mathcal{W}\left[1 + f\text{tanh}\left( p (\mathcal{T} - \mathcal{F}) \right) \right]\]

    This weighting limits each update to a relative change of \(\pm f\), passed as "feedback_factor", which is useful to prevent large changes. The speed of correction is controlled by \(p\), the power passed as "feedback_exponent".

• Conjugate Gradient (CG) phase retrieval.

  • 'CG'

    (This feature is experimental.)

    Some holography—especially that with more complicated holographic objectives—can be better treated with gradient-based methods. In these cases, the phase is guided to an optimized state by following the back-propagated gradients (with respect to phase) of given objective loss which is passed as one of the flags to optimize(). Weighting different components of the objective leads to tradeoffs between those components: for instance a tradeoff between power guided into a given pattern and the uniformity of the realized pattern. slmsuite uses pytorch as a backend for gradient computation. Notably, memory is still owned and initialized by cupy, but gradients can be calculated by using pytorch-cupy interoperability.

    The objective loss is expected to be a torch.nn.Module and defaults to a complex variant of torch.nn.MSELoss(). loss is called in the style of pytorch, using (as arguments) the computed farfield (with gradient tree intact) and the target values for the farfield. Internally, this looks like:

    result = loss(      # The user provides this nn.Module to .optimize()
        farfield,       # The farfield (with gradients), calculated from `phase` by slmsuite
        target          # The target, initialized by the user and processed by slmsuite
    )
    result.backward()   # Gradients are back-propagated to the input `phase`.
    

    For FeedbackHologram and subclasses, the gradients are computed computationally, but the computational values are then replaced with the experimental results. This allows optimization of the experimental results using the computational gradients (correct to first order) as a guide. Currently, feedback is not supported for spot arrays with "experimental_spot" or "computational_spot" feedback (WGS probably works better for such spot array objectives anyway).

    Creating a custom objective is as simple as making a custom torch.nn.Module.forward() method. These methods can be as simple as a single expression or as complicated as a full neural network operating on the input parameters. However, remember to use pytorch methods because the arguments are of type torch.Tensor. Here’s an example of a custom torch.nn.Module.forward() which implements the Huber loss:

    # Define the loss as a class.
    class HuberLoss(nn.Module):
        def __init__(self, delta=1.0):
            super(HuberLoss, self).__init__()
            self.delta = delta
    
        def forward(self, farfield, target):
            residual = torch.abs(farfield - target)
            quadratic = torch.clamp(residual, max=self.delta)
            linear = residual - quadratic
            loss = 0.5 * quadratic ** 2 + self.delta * linear
    
            return torch.mean(loss)
    
    # Initialize the class. Remember that we can pass arguments (delta) here.
    loss = HuberLoss(delta=2.0)
    
    # Pass the loss to the hologram by one of two methods:
    hologram.optimize(..., loss=loss)       # 1. Pass as **kwarg.
    hologram.flags["loss"] = loss           # 2. Set directly.
    

    MRAF (next section), if desired, needs to be handled by the loss function. MRAF information is encoded in the target, with the noise region being nan.

• The option for Mixed Region Amplitude Freedom (MRAF) feedback. In standard iterative algorithms, the entire Fourier-domain unpatterned field is replaced with zeros. This is disadvantageous because a desired farfield pattern might not be especially compatible with a given nearfield amplitude, or otherwise. MRAF enables “noise regions” where some fraction of the given farfield is not replaced with zeros and instead is allowed to vary. In practice, MRAF is enabled by setting parts of the target to nan; these regions act as the noise regions. The "mraf_factor" flag in flags allows the user to partially attenuate the noise regions. A factor of 0 fully attenuates the noise region (normal WGS behavior). A factor of 1 does not attenuate the noise region at all (the default). Middle ground is recommended, but is application-dependent as a tradeoff between improving pattern fidelity and maintaining pattern efficiency.

  As examples, consider two cases where MRAF can be useful:

  • Sloping a top hat. Suppose we want very flat amplitude on a beam. Requesting a sharp edge to this beam can lead to fringing effects at the boundary which mitigate flatness both inside and outside the beam. If instead a noise region is defined in a band surrounding the beam, the noise region will be filled with whatever slope best enables the desired flat beam.

  • Mitigating diffractive orders. Without MRAF, spot patterns with high crystallinity often have “ghost” diffractive orders which continue the pattern past the edges of requested spots. Even though these orders are attenuated during each phase retrieval iteration, they remain part of the best solution for the recovered phase. With MRAF, a noise region can help solve for retrieved phase which does not generate these undesired orders.

Caution

Requesting stat_groups will slow the speed of optimization due to the overhead of processing and saving statistics, especially in the case of GPU-accelerated optimization where significant time cost is incurred by moving these statistics to the CPU. This is especially apparent in the case of fully-computational holography, where this effect can slow what is otherwise a fully-GPU-contained loop by an order magnitude.

Tip

This function uses a parameter naming convention borrowed from scipy.optimize.minimize() and other functions in scipy.optimize. The parameters method, maxiter, and callback have the same functionality as the equivalently-named parameters in scipy.optimize.minimize().

Parameters:

• method (str) – Optimization method to use. See the list of optimization methods above.

• maxiter (int) – Number of iterations to optimize before terminating.

• verbose (bool OR int) – Whether to display tqdm progress bars. These bars are also not displayed for maxiter <= 1. If verbose is greater than 1, then flags are printed as a preamble.

• callback (callable OR None) – Same functionality as the equivalently-named parameter in scipy.optimize.minimize(). callback must accept a Hologram or Hologram subclass as the single argument. If callback returns True, then the optimization exits. Ignored if None.

• feedback (str OR None) –

  Type of feedback to use during optimization, for instance when weighting in "WGS". For direct instances of Hologram, this can only be "computational" feedback. Subclasses support more types of feedback. Supported feedback options include the following:

  • "computational" Uses the the projected farfield pattern (transform of the complex nearfield) as feedback.

  • "experimental" Uses a camera contained in a passed cameraslm as feedback. Specific to subclasses of FeedbackHologram.

  • "computational_spot" Takes the computational result (the projected farfield pattern) and integrates regions around the expected positions of spots in an optical focus array. More stable than "computational" for spots. Specific to subclasses of SpotHologram.

  • "experimental_spot" Takes the experimental result (the image from a camera) and integrates regions around the expected positions of spots in an optical focus array. More stable than "experimental" for spots. Specific to subclasses of SpotHologram.

  • "external_spot" Uses some external user-provided metric for spot feedback. See external_spot_amp. Specific to subclasses of SpotHologram.

• stat_groups (list of str OR None) – Strings representing types of feedback (data gathering) upon which statistics should be derived. These strings correspond to valid types of feedback (see above). For instance, if "experimental" is passed as a stat group, statistics on the pixels in the experimental feedback image will automatically be computed and stored for each iteration of optimization. However, this comes with overhead (see above warning).

• **kwargs (dict, optional) – Various weight keywords and values to pass depending on the weight method. These are passed into flags. See options documented in the constructor.

optimize_cg(iterations, callback)

Conjugate Gradient (CG) iterative phase retrieval.

(This feature is experimental.)

Solves the “phase problem”: approximates the nearfield phase that transforms a known nearfield source amplitude to a desired farfield target amplitude.

Caution

This function should be called through optimize() and not called directly. It is left as a public function exposed in documentation to clarify how the internals of optimize() work.

Parameters:

• iterations (iterable) – Number of loop iterations to run. Is an iterable to pass a tqdm iterable.

• callback (callable OR None) – See optimize().

optimize_gs(iterations, callback)

GPU-accelerated Gerchberg-Saxton (GS) iterative phase retrieval.

Solves the “phase problem”: approximates the nearfield phase that transforms a known nearfield source amplitude to a desired farfield target amplitude.

Caution

This function should be called through optimize() and not called directly. It is left as a public function exposed in documentation to clarify how the internals of optimize() work.

Note

Default FFTs are not in-place in this algorithm. In both non-cupy and cupy implementations, numpy.fft does not support in-place operations. However, scipy.fft does in both. In the future, we may move to the scipy implementation. However, neither numpy or scipy fftshift support in-place movement (for obvious reasons). For even faster computation, algorithms should consider not shifting the FFT result, and instead shifting measurement data / etc to this unshifted basis. We might also implement get_fft_plan for even faster FFTing. However, in practice, speed is limited by other peripherals (especially feedback and stats) rather than FFT speed or memory.

Parameters:

• iterations (iterable) – Number of loop iterations to run. Is an iterable to pass a tqdm iterable.

• callback (callable OR None) – See optimize().

plot_farfield(source=None, title='', limits=None, units='knm', limit_padding=0.1, figsize=(8, 4), cbar=False)

Plots an overview (left) and zoom (right) view of source.

Parameters:

• source (array_like OR None) – Should have shape equal to shape. If None, defaults to amp_ff.

• title (str) – Title of the plots. If "phase" is a substring of title, then the source is treated as a phase.

• limits (((float, float), (float, float)) OR None) – \(x\) and \(y\) limits for the zoom plot in "knm" space. If None, limits are autocomputed as the smallest bounds that show all non-zero values (plus limit_padding). Note that autocomputing on target will perform well, as zero values are set to actually be zero. However, doing so on computational or experimental outputs (e.g. amp_ff) will likely perform poorly, as values in the field deviate slightly from zero and artificially expand the limits.

• units (str) – Far-field units for plots (see convert_vector() for options). If units requiring a SLM are desired, the attribute cameraslm must be filled.

• limit_padding (float) – Fraction of the width and height to expand the limits of the zoom plot by, only if the passed limits is None (autocompute).

• figsize (tuple) – Size of the plot.

• cbar (bool) – Whether to add colorbars to the plots. Defaults to False.

Returns:

Used limits, which may be autocomputed. Autocomputed limits are returned as integers.

Return type:

((float, float), (float, float))

plot_nearfield(source=None, title='', padded=False, figsize=(8, 4), cbar=False)

Plots the amplitude (left) and phase (right) of the nearfield (plane of the SLM). The amplitude is assumed (whether uniform, or experimentally computed) while the phase is the result of optimization.

Parameters:

• title (str) – Title of the plots.

• padded (bool) – If True, shows the full computational nearfield of shape shape. Otherwise, shows the region at the center of the computational space of size slm_shape corresponding to the unpadded SLM.

• figsize (tuple) – Size of the plot.

• cbar (bool) – Whether to add colorbars to the plots. Defaults to False.

plot_stats(stats_dict=None, stat_groups=[], ylim=None, show=False)

Plots the statistics contained in the given dictionary.

Parameters:

• stats_dict (dict OR None) – Stats to plot in dictionary form. If None, defaults to stats.

• stat_groups (list of str OR None) – Which statistics groups to plot. If empty or None is provided, defaults to all groups present in stats.

• ylim ((int, int) OR None) – Allows the user to pass in desired y limits. If None, the default y limits are used.

• show (bool) – Whether or not to immediately show the plot. Defaults to false.

remove_vortices(plot=False)

Removes the computed phase vortices in the farfield where the target amplitude is positive. Useful for smoothing out the pattern and reducing speckle. The user can call this method by passing a callback= function containing it. For instance:

# Define a function to use a callback.
def remove_vortices_callback(holo):
    if holo.iter % 10 == 9:     # Only remove vortices every 10 iterations.
        holo.remove_vortices()  # This method is slightly expensive, so calling every loop is not advised.

# The function will be called during the loop.
hologram.optimize(..., callback=remove_vortices_callback)

Important

This callback can only applied be during a GS loop. To use for a conjugate gradient hologram, do a single iteration of GS.

Parameters:

plot (bool) – Enable debug plots.

reset(reset_phase=True, reset_flags=False)

Resets the hologram to an initial state. Does not restore the preconditioned phase that may have been passed to the constructor (as this information is lost upon optimization). Instead, phase is randomized if reset_phase=True. Also uses the current target rather than the target that may have been passed to the constructor (e.g. includes current refine_offset() changes, etc).

Parameters:

• reset_phase (bool) – Whether to additionally call reset_phase().

• reset_flags (bool:) – Whether to erase the information (including passed kwargs) stored in flags.

reset_phase(custom_phase=None, random_phase=None, quadratic_phase=None)

Resets the hologram to a provided phase, to a random state, or to a quadratic phase which overlaps with the target pattern.

Parameters:

• custom_phase (array_like OR None) – Custom nearfield initial phase. If not None, then all other parameters are ignored. See phase. phase should only be passed if the user wants to precondition the optimization. Of shape slm_shape.

• random_phase (float OR None) – Sets the phase to uniformly random phase, scaled to \(2\pi\). Setting random_phase to a fraction of 1 likewise scales the randomness. If None, looks for "random_phase" in flags. This adds with the quadratic_phase parameter.

• quadratic_phase (bool OR float OR None) – We can also precondition the phase analytically (with a lens and blaze) to roughly the size of the target hologram, according to the first and second order image_moments(). This quadratic preconditioning is thought to help reduce the formation of optical vortices or speckle compared to random initialization, as the analytic distribution is smooth in phase. If None, looks for "quadratic_phase" in flags. If a float is provided, the size of the beam in the farfield is scaled accordingly. This feature is ignored if phase is not None.

reset_weights()

Resets the hologram weights to the target defaults.

save_stats(file_path, include_state=True)

Uses save_h5() to export the statistics hierarchy to a given h5 file.

Parameters:

• file_path (str) – Full path to the file to read the data from.

• include_state (bool) – If True, also includes all other attributes of Hologram except for dtype (cannot pickle) and amp_ff (can regenerate). These attributes are converted to numpy if necessary. Note that the intent is not to produce a runnable Hologram by default (as this would require pickling hardware interfaces), but rather to provide extra information for debugging.

static set_mempool_limit(device=0, size=None, fraction=None)

Helper function to set the cupy memory pool size.

Parameters:

• device (int) – Which GPU to set the limit on. Passed to cupy.cuda.Device().

• size (int) – Desired number of bytes in the pool. Passed to cupy.cuda.MemoryPool.set_limit().

• fraction (float) – Fraction of available memory to use. Passed to cupy.cuda.MemoryPool.set_limit().

set_target(new_target, reset_weights=False)

Change the target to something new. This method handles cleaning and normalization.

Parameters:

• new_target (array_like OR None) – New target to optimize towards. Should be of shape shape. If None, target is zeroed (used internally, but probably should not be used by a user).

• reset_weights (bool) – Whether to update the weights to this new target.