class CTF {

  private:
    float spherical_aberration;
    float wavelength;
    float amplitude_contrast;
    float defocus_1;
    float defocus_2;
    float defocus_half_range;
    float astigmatism_azimuth;
    float additional_phase_shift;
    float sample_thickness; // pixels
    float beam_tilt_x; // rad
    float beam_tilt_y; // rad
    float beam_tilt; // rad
    float beam_tilt_azimuth; // rad
    float particle_shift_x; // pixels
    float particle_shift_y; // pixels
    float particle_shift; // A
    float particle_shift_azimuth; // rad
    // Fitting parameters
    float lowest_frequency_for_fitting;
    float highest_frequency_for_fitting;
    float astigmatism_tolerance;
    float highest_frequency_with_good_fit;
    // Precomputed terms to make evaluations faster
    float precomputed_amplitude_contrast_term;
    float squared_wavelength;
    float cubed_wavelength;
    float low_resolution_contrast;

    float squared_illumination_aperture;
    float squared_energy_half_width;

  public:
    // Constructors, destructors
    CTF( );
    CTF(float acceleration_voltage,
        float spherical_aberration,
        float amplitude_contrast,
        float defocus_1,
        float defocus_2,
        float astigmatism_azimuth,
        float lowest_frequency_for_fitting,
        float highest_frequency_for_fitting,
        float astigmatism_tolerance,
        float pixel_size,
        float additional_phase_shift,
        float beam_tilt_x      = 0.0f,
        float beam_tilt_y      = 0.0f,
        float particle_shift_x = 0.0f,
        float particle_shift_y = 0.0f,
        float sample_thickness = 0.0f);

    CTF(float wanted_acceleration_voltage, // keV
        float wanted_spherical_aberration, // mm
        float wanted_amplitude_contrast,
        float wanted_defocus_1_in_angstroms, // A
        float wanted_defocus_2_in_angstroms, // A
        float wanted_astigmatism_azimuth, // degrees
        float pixel_size, // A
        float wanted_additional_phase_shift_in_radians, // rad
        float wanted_beam_tilt_x_in_radians        = 0.0f, // rad
        float wanted_beam_tilt_y_in_radians        = 0.0f, // rad
        float wanted_particle_shift_x_in_angstroms = 0.0f, // A
        float wanted_particle_shift_y_in_angstroms = 0.0f, // A
        float wanted_sample_thickness_in_nms       = 0.0f); // nm

    ~CTF( );

    void Init(float wanted_acceleration_voltage_in_kV, // keV
              float wanted_spherical_aberration_in_mm, // mm
              float wanted_amplitude_contrast,
              float wanted_defocus_1_in_angstroms, // A
              float wanted_defocus_2_in_angstroms, //A
              float wanted_astigmatism_azimuth_in_degrees, // degrees
              float wanted_lowest_frequency_for_fitting_in_reciprocal_angstroms, // 1/A
              float wanted_highest_frequency_for_fitting_in_reciprocal_angstroms, // 1/A
              float wanted_astigmatism_tolerance_in_angstroms, // A. Set to negative to indicate no restraint on astigmatism.
              float pixel_size_in_angstroms, // A
              float wanted_additional_phase_shift_in_radians, //rad
              float wanted_beam_tilt_x_in_radians        = 0.0f, // rad
              float wanted_beam_tilt_y_in_radians        = 0.0f, // rad
              float wanted_particle_shift_x_in_angstroms = 0.0f, // A
              float wanted_particle_shift_y_in_angstroms = 0.0f, // A
              float wanted_sample_thickness_in_nms       = 0.0f); // nm

    void Init(float wanted_acceleration_voltage_in_kV, // keV
              float wanted_spherical_aberration_in_mm, // mm
              float wanted_amplitude_contrast,
              float wanted_defocus_1_in_angstroms, // A
              float wanted_defocus_2_in_angstroms, //A
              float wanted_astigmatism_azimuth_in_degrees, // degrees
              float pixel_size_in_angstroms, // A
              float wanted_additional_phase_shift_in_radians, // rad
              float wanted_sample_thickness_in_nms = 0.0f); //nm

    void SetDefocus(float wanted_defocus_1_pixels, float wanted_defocus_2_pixels, float wanted_astigmatism_angle_radians);
    void SetAdditionalPhaseShift(float wanted_additional_phase_shift_radians);
    void SetEnvelope(float wanted_acceleration_voltage, float wanted_pixel_size_angstrom, float dose_rate);
    void SetBeamTilt(float wanted_beam_tilt_x_in_radians, float wanted_beam_tilt_y_in_radians, float wanted_particle_shift_x_in_pixels = 0.0f, float wanted_particle_shift_y_in_pixels = 0.0f);
    void SetHighestFrequencyForFitting(float wanted_highest_frequency_in_reciprocal_pixels);
    void SetLowResolutionContrast(float wanted_low_resolution_contrast);
    void SetSampleThickness(float wanted_sample_thickness_in_pixels);

    inline void SetHighestFrequencyWithGoodFit(float wanted_frequency_in_reciprocal_pixels) { highest_frequency_with_good_fit = wanted_frequency_in_reciprocal_pixels; };

    //
    std::complex<float> EvaluateComplex(float squared_spatial_frequency, float azimuth);
    float               Evaluate(float squared_spatial_frequency, float azimuth);
    float               EvaluatePowerspectrumWithThickness(float squared_spatial_frequency, float azimuth);

    float               EvaluateWithEnvelope(float squared_spatial_frequency, float azimuth);
    float               PhaseShiftGivenSquaredSpatialFrequencyAndAzimuth(float squared_spatial_frequency, float azimuth);
    std::complex<float> EvaluateBeamTiltPhaseShift(float squared_spatial_frequency, float azimuth);
    float               PhaseShiftGivenBeamTiltAndShift(float squared_spatial_frequency, float beam_tilt, float particle_shift = 0.0f);
    float               PhaseShiftGivenSquaredSpatialFrequencyAndDefocus(float squared_spatial_frequency, float defocus);
    float               DefocusGivenAzimuth(float azimuth);
    float               BeamTiltGivenAzimuth(float azimuth);
    float               ParticleShiftGivenAzimuth(float azimuth);
    float               WavelengthGivenAccelerationVoltage(float acceleration_voltage);

    // This is the sinc(xi) term derived in the supplemental of McMullan et al. (2015)
    inline float IntegratedDefocusModulation(float squared_spatial_frequency) {
        return sinc(PIf * wavelength * squared_spatial_frequency * sample_thickness);
    };

    inline float GetLowestFrequencyForFitting( ) { return lowest_frequency_for_fitting; };

    inline float GetHighestFrequencyForFitting( ) { return highest_frequency_for_fitting; };

    inline float GetHighestFrequencyWithGoodFit( ) { return highest_frequency_with_good_fit; };

    inline float GetAstigmatismTolerance( ) { return astigmatism_tolerance; };

    inline float GetAstigmatism( ) { return defocus_1 - defocus_2; };

    bool IsAlmostEqualTo(CTF* wanted_ctf, float delta_defocus = 100.0f);
    bool BeamTiltIsAlmostEqualTo(CTF* wanted_ctf, float delta_beam_tilt = 0.00001f);
    void EnforceConvention( );
    void PrintInfo( );
    void CopyFrom(CTF other_ctf);
    void ChangePixelSize(float old_pixel_size, float new_pixel_size);

    inline float GetDefocus1( ) { return defocus_1; };

    inline float GetDefocus2( ) { return defocus_2; };

    inline float GetBeamTiltX( ) { return beam_tilt_x; };

    inline float GetBeamTiltY( ) { return beam_tilt_y; };

    inline float GetSphericalAberration( ) { return spherical_aberration; };

    inline float GetAmplitudeContrast( ) { return amplitude_contrast; };

    inline float GetAstigmatismAzimuth( ) { return astigmatism_azimuth; };

    inline float GetAdditionalPhaseShift( ) { return additional_phase_shift; };

    inline float GetWavelength( ) { return wavelength; };

    int   ReturnNumberOfExtremaBeforeSquaredSpatialFrequency(float squared_spatial_frequency, float azimuth);
    float ReturnSquaredSpatialFrequencyGivenPhaseShiftAndAzimuth(float phase_shift, float azimuth);
    float ReturnSquaredSpatialFrequencyOfAZero(int which_zero, float azimuth, bool inaccurate_is_ok = false);
    float ReturnSquaredSpatialFrequencyOfPhaseShiftExtremumGivenAzimuth(float azimuth);
    float ReturnSquaredSpatialFrequencyOfPhaseShiftExtremumGivenDefocus(float defocus);
    float ReturnPhaseAberrationMaximum( );
    float ReturnPhaseAberrationMaximumGivenDefocus(float defocus);
};
