We consider the optimal pulse duration and repetition rate of MIR and visible light for wide-field MIP imaging by exploiting thermal conduction simulations (see Methods for details). Thermal diffusion causes degradation of spatial resolution and saturation/decay of the amount of signals in the MIP imaging. The change in optical phase-delay of visible light due to the local temperature rise, which we call the MIP phase change, is expressed as

where x, y, z denote spatial coordinates, t the time, λ the wavelength of visible light, dn/dT the thermo-optic coefficient of the sample, and ΔT the local temperature change. The temporal evolution of the MIP phase change under various MIR excitation conditions in an aqueous environment is calculated by solving the 3D heat conduction equation,

where ν denotes the thermal diffusivity, I the pulse fluence per unit time, α the absorbance, ρ the density, c_p the specific heat capacity.

To derive the optimal pulse duration of MIR light, we calculate the spread of the spatial profile (Fig. 1a) and the phase change (Fig. 1b) in the MIP phase change image with respect to the pulse duration of MIR light. We assume the initial heat spots (target objects) are spheres with a diameter of 500 nm, 2 µm, and 10 µm in aqueous environments. They have the same thermal diffusivity as water and are continuously heated by the MIR pulse with constant peak power, which represents a situation using a QCL, illustrating the disadvantages of using long pulses. We assume that the visible probe pulse is sufficiently shorter than the MIR pulse and illuminated at the end of the MIR pulse. Figure 1e shows the timing chart of the MIR and visible pulses. The results show that a longer pulse builds up the MIP phase change, but too much elongation leads to degradation of the spatial resolution and signal saturation due to thermal diffusion, particularly for small objects with a large surface/volume ratio. The saturation time is proportional to the square of its radius. For example, when observing the 500-nm object, a 100-ns MIR pulse deteriorates the spatial resolution by a factor of 1.3 (Fig. 1a). Some works exploit a CW MIR light source

Fig 1  Derivation of optimal pulse duration and repetition rate of MIR and visible light by thermal conduction simulations.

a Degradation of the spatial resolution in MIP imaging originating from thermal diffusion depending on the MIR pulse duration. The horizontal axis is the MIR pulse duration, and the vertical axis is the ratio of the e⁻² radius in the MIP phase change image and the radius of the original spheres. b Saturation of the MIP phase change depending on the MIR pulse duration. MIP phase changes at the centers of the spheres are plotted against MIR pulse durations, which are normalized by that with the MIR pulse duration of 10 ns. The probe delay time after MIR excitation is 0 s for (a) and (b). c Degradation of the spatial resolution in MIP imaging originating from thermal diffusion depending on the probe delay time after MIR excitation. d Decay of the MIP phase change depending on the probe delay time after MIR excitation. The MIP phase changes are normalized by that with the probe delay of 0 s. MIR pulse duration is set to 10 ns for (c) and (d). e Pulse duration and timing chart of the MIR and visible pulses. f Temporal decay of the MIP phase change for water (10 µm thickness) sandwiched between two CaF₂ substrates. The vertical axis shows the MIP phase change at the center of the heated spot. The pulse duration of the MIR light is assumed to be much shorter than the thermal decay time. The spatial distribution of the MIP phase change is assumed as a gaussian function (FWHM = 91 µm) along the x- and y-axes, determined by the intensity profile of the MIR spot, and an exponential function along the z-axis that decays after 16 µm, which is derived from the Lambert-Beer law

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Next, to derive the optimal pulse duration and delay of the visible light, we calculate the spread of the spatial profile (Fig. 1c) and the phase change (Fig. 1d) in the MIP phase change image with respect to the delay of the visible probe light from the end of the MIR excitation. In this calculation, the MIR pulse duration is 10 ns, and the visible probe pulse is sufficiently shorter than the MIR pulse. The results show that the probe delays longer than 10 ns cause degrading the spatial resolution (Fig. 1c) and decreasing the phase change (Fig. 1d) of the MIP phase change image. For example, when observing the 500-nm object with a delay of 100 ns, the radius of the MIP phase change becomes 1.9-times larger than the object, and the MIP phase change decays to 50% of that with a delay of 0 s. This simulation shows that it is desirable for visible probe pulses to have a similar or shorter pulse duration than MIR pulses, i.e., < 10 ns, with the delay time shorter than the pulse duration. This result indicates that visible light sources that pose difficulties in ensuring pulse energy, such as LEDs, are not the optimal probes for the MIP effect.

Finally, to derive the optimal pulse repetition rate, we calculate the thermal diffusion time of a heated spot with an FWHM diameter of 91 µm in an aqueous environment which reflects the condition of our following experiment (Fig. 1f). Note that, when measuring cells, the thermal diffusion time over the entire FOV does not depend on the size of the target objects but on the spot size of MIR light due to water absorption. To avoid potential thermal damage to samples due to a thermal pile-up, the induced photothermal heat should be diffused off when the next MIR pulse arrives at the sample. The result shows that this condition is sufficiently achieved at 1 ms after the arrival of the first MIR pulse. Hence, it is desirable for wide-field single-cell imaging to exploit a pulse repetition rate of ~1 kHz.

Supplementary Note 1 compiles the parameters of existing wide-field systems, which allows for comparative analyses. For example, the MIR pulse energies in Table S1 can be used for estimating MIP phase change induced by different MIR light sources, such as a pulsed OPO, a pulsed QCL, and a CW QCL, based on the knowledge provided by the simulation results shown in Fig. 1b (see Supplementary Note 1 for details). Table S1 shows that the previously demonstrated systems do not satisfy the optimal condition determined by our simulations.

The principle and the schematic of our newly developed MIP-QPI are shown in Fig. 2. MIR light with a narrow spectral width at a certain wavenumber is irradiated widely over the sample. Resonant molecules absorb the MIR light and are excited to their vibrational states. The molecular vibrations relax by transferring their energy to the surrounding medium in the form of heat, causing thermal expansion and thus a change in local density. The resulting change in refractive index in the vicinity of the target molecules (i.e., MIP effect) is captured as a change in optical phase delay of the transmitted visible light in the QPI system

Fig 2  Principle and schematic of MIP-QPI.

a Principle of MIP-QPI. b Optical system of high-SNR MIP-QPI. c Timing chart of MIR and visible pulses. MIR mid-infrared, LBO LiB₃O₅, SHG second harmonic generation, PPLN periodically poled lithium niobate, OPO optical parametric oscillator

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Figure 2b shows the schematic of our MIP-QPI system developed in this study. Two Nd: YAG Q-switched lasers (1064-nm wavelength, 1-kHz repetition rate, 6-ns pulse duration) (NL204, Ekspla) are used to generate visible and MIR pulses via nonlinear wavelength conversions. The visible light pulses (532-nm wavelength, 1-kHz repetition rate, 5-ns pulse duration) are provided by second harmonic generation (SHG) with a 15-mm-long LBO crystal. The MIR light pulses (2800–3250 cm⁻¹ wavenumber tunable, 1-kHz repetition rate, 9-ns pulse duration, ~10-µJ pulse energy) are obtained as idler pulses of a homemade high-intensity nanosecond OPO with a fan-out PPLN crystal

We describe the performance of our homemade ns-PPLN-OPO (see Supplementary Note 3 for details). The crystal is a 50-mm-long fan-out PPLN with a poling period varying from 27.5 to 31.6 µm stabilized at 40 ℃. The pulse energy of the pump light from the Nd: YAG Q-switched laser is ~100 µJ. The OPO cavity is resonant with the NIR signal pulses (5950–6800 cm⁻¹ tunable), and only the MIR idler pulses (2600–3450 cm⁻¹ tunable) are extracted with a long-pass filter after the cavity. Figure 3a shows the relationship between the MIR wavenumber and the idler pulse energy, which is ~10 µJ between 2800 and 3250 cm⁻¹. Figure 3b shows the spectrum of MIR light measured by a homemade FTIR spectrometer. The FWHM of the spectrum is ~10 cm⁻¹ at each MIR wavenumber, which determines the spectral resolution and is sufficient to resolve absorption peaks of CH₃ and CH₂ stretching modes (the modes are 20 ~ 30 cm⁻¹ apart from each other)

Fig 3  Basic performances of MIR light source (ns-OPO).

a MIR pulse energy in the range of 2800–3250 cm⁻¹. b Spectra of MIR light measured with a homemade FTIR spectrometer. The red points indicate the FWHM of each spectrum. c Linearity of MIP phase change with respect to MIR fluence for a water sample excited at 2918 cm⁻¹. d Temporal decay of MIP phase change for a water sample with an excitation area of 69 µm × 69 µm. FWHM full width at half maximum

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We discuss noise reduction in phase measurement with QPI by employing a high full-well-capacity image sensor and a high-intensity ns visible light. If the system is mechanically stable enough, the temporal phase noise in QPI can be dominated by optical shot noise. Thus, the precision becomes higher when more light enters the image sensor. The full-well capacity of the image sensor used in our system is 2 Me⁻ pixel⁻¹ (Q-2HFW, Adimec), which is 200 times larger than that of a conventional CMOS image sensor (10 ke⁻ pixel⁻¹, e.g., acA2440–75um, Basler). We perform the following evaluations of the noise reduction.

We examine the dependence of temporal phase noise on the average number of electrons contributing to the reconstruction of the phase images (=N_electron) per sensor's pixel (Fig. 4a), that is, the average number of electrons in the holograms (see Supplementary Note 4 for the calculation method). The maximum value of N_electron is determined as half the full-well capacity of the image sensor. Note that N_electron equals the number of incident photons multiplied by the quantum efficiency of the image sensor. We record 100 holograms without a sample and calculate the differences in phase images between adjacent frames. Then, the temporal standard deviation (STD) of the 50 differential images is calculated at each pixel, and the average value of 80 pixels × 80 pixels in the temporal STD map is evaluated as the temporal phase noise. The number of electrons per pixel is estimated from the sensor's digital output value and the full-well capacity. The data points on the left side of the graph are the measurement results using the conventional 10k-e⁻ image sensor, which is in good agreement with the theoretically estimated phase noise limited by optical shot noise (orange line)

Fig 4  Noise reduction in phase measurement with QPI.

a Dependence of temporal phase noise on the number of electrons generated in image sensors. Red and blue dots are measured data with a conventional 10k-e⁻ image sensor (acA2440–75um, Basler) on the left side and a high full-well-capacity 2M-e⁻ image sensor (Q-2HFW, Adimec) on the right side, respectively. Orange and green lines are theoretically estimated phase noise from Eq. 3 in "Methods" with sensor noise σ_sensor = 0, and the purple line is that with σ_sensor = 572 e⁻ (detailed parameters are written in Methods). b Comparison between MIP images taken with the two sensors: phase images (top) and MIP phase change images (bottom) of live COS7 cells taken with 10k-e⁻ (left) and 2M-e⁻ (right) sensors. The number of electrons per pixel^, N_electron, is 2.82 × 10³ e⁻ and 2.34 × 10⁵ e⁻ with 10k-e⁻ and 2M-e⁻ sensors, respectively. MIR light at a wavenumber of 2975 cm⁻¹ is irradiated on a spot size of 80 μm × 80 μm with a fluence of 1.1 nJ µm⁻²

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Next, we compare the SNR of single-frame MIP phase change images of live cells measured with the two image sensors. Figure 4b shows results for the observation of COS7 cells exploiting MIR light with a wavenumber of 2975 cm⁻¹, a spot size of 80 μm × 80 μm, and pulse energy of 7.1 µJ. The background MIP phase change image of water without cells is subtracted to make the intracellular structures more visible. The spatial STD of 20 pixels × 20 pixels inside the blue box is defined as the phase noise. Note that Fig. 4b has ~√2-times larger noise than the temporal phase noise in Fig. 4a due to the background subtraction process. In the case of the 10k-e⁻ sensor, the MIP phase change is buried in the phase noise, whereas in the case of the 2M-e⁻ sensor, intracellular structures such as nucleoli and lipid droplets are clearly seen. The phase noise is 12.2 mrad for the former sensor and 1.6 mrad for the latter (8.6 mrad and 1.1 mrad without water background subtraction, respectively). We verify that the high full-well capacity sensor provides ~7.6-times reduction in phase noise with 85-times higher power of visible light for the live-cell imaging.

We demonstrate MIP imaging of a live COS7 cell at 50 fps. Figure 5a is a phase image measured in MIR-OFF state, and 5b and c are MIP phase change images with water background subtraction, excited at 2925, and 3188 cm⁻¹ MIR wavenumbers, respectively. Note that they are all single-frame images without averaging. The MIR pulse energy at the sample plane is ~6.5 μJ with a spot size of 87 μm × 87 μm. The image at 2925 cm⁻¹ contains strong signals mainly from CH₂ bonds of lipid droplets indicated by the white arrow, while the image at 3188 cm⁻¹ shows signals that hardly reflect intracellular structures. Thus, different contrasts are observed at different MIR wavenumbers at an unprecedentedly high measurement rate of 50 Hz (20 ms measurement time per image). The phase noise, i.e., the spatial STD of 20 pixels × 20 pixels inside the blue box in Fig. 5b, is evaluated as 1.6 mrad with water background subtraction by following the procedure used in Fig. 4. Since the signal from the lipid droplets is ~100 mrad, the SNR is 63 (89 without water background subtraction). Hence, high-SNR live-cell MIP imaging beyond video rate is achieved for the first time.

Fig 5  Video-rate MIP imaging of a live COS7 cell.

a A phase image. b, c Single-frame MIP phase change images excited at 2925 and 3188 cm⁻¹ with a spot size of 87 µm × 87 µm. The images are taken at a rate of 50 Hz (20 ms measurement time per image)

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To exemplify the capabilities of high-speed MIP imaging for more practical cellular dynamics, we observe cellular dynamics on a sub-second scale, specifically, the transfer of water molecules through aquaporins—membrane proteins that function as water-selective channels and control the intracellular water content

Figure 6a illustrates a schematic diagram of the measurement platform, wherein a capillary filled with H₂O-based phosphate-buffered saline (PBS) is exchanged for D₂O-based PBS via a syringe pump within a time frame shorter than the sensor's frame interval. We present a series of images depicting temporal evolutions in MIP phase change recorded at 50 fps (Fig. 6b). The measured movie can be seen in Supplementary Video 1. Between −100 and 0 ms, an H₂O-induced MIP phase change reflecting the MIR spot is visibly apparent. From 0 to 300 ms, the extracellular signal promptly declines upon substitution with D₂O-based PBS, and only the intracellular MIP signal produced by H₂O molecules remains, which eventually decays over the course of several hundred milliseconds. Figure 6c, d display the phase image of the cell in the MIR OFF state and the temporal decay of MIP phase changes at various sites indicated in Fig. 6c, respectively. The signal fluctuation around 100 ms in Fig. 6d is an artifact caused by slight agitation of the capillary during the liquid exchange process, which can be resolved through refinement of the capillary fixation. The sites exhibiting larger phases, i.e., thicker cellular sites, manifest slower decay, as the imaging was performed in the presence of both water and cells in the z-direction, resulting in different ratios of the two signal types (dot squares in Fig. 6a). In order to estimate the intracellular decay time at each site, the height distribution inferred from the phase information and the extracellular decay time are substituted for Eq. 4, described in Methods, prior to the fitting procedure. The intracellular decay time is found to be nearly constant within the central portions of the cells, with an average of 420 ms within the square region depicted in Fig. 6e. When investigating the function of aquaporins, it is important to determine the velocity of water molecules traversing the cell membrane, P_d, because the decay time, τ, varies in accordance with the shape and size of the cell. In the previous study

Fig 6  Video-rate MIP imaging of an H₂O/D₂O exchange in a live COS7 cell through aquaporins.

a A schematic of the measurement platform, wherein H₂O-based PBS filled in a capillary is exchanged for D₂O-based PBS via a syringe. A percentage of the cell's space occupation along the z-axis of the capillary varies depending on the detection regions, denoted by dot squares. b Series of MIP images at 3014 cm⁻¹ recorded at 50 fps. c A phase image. d The average temporal decay within the square regions in Fig. 6c, normalized by the MIP phase change at −100 ms. e A distribution of intracellular decay times (τ in Eq. 4) derived from fitting temporal decays. The fitting range is chosen on the longer side of the dotted line shown in Fig. 6d in order to circumvent the signal fluctuation around 100 ms

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We measure spectra of a single live COS7 cell and perform multivariate analysis as one of the applications utilizing the high SNR of our system. By scanning the wavenumber of the MIR light, 40 MIP phase change images are acquired in the range of 2800 ~ 3250 cm⁻¹. The MIR pulse energy at the sample plane is ~6.5 μJ with a spot size of 85 μm × 85 μm. The total acquisition time is ~10 min for 500 MIP phase change images averaged at each wavenumber, which is limited by the performance of the controlling system for spectral acquisition (see Discussion for more details). The hyperspectral data are subjected to multivariate analysis (Multivariate curve resolution, MCR)

Figure 7a–c, d, e, and f shows spatial distributions of the three MCR components, a phase image in a MIR-OFF state, a merged image of the three MCR images, and spectra of the three MCR components, respectively. In MCR1, the MIP contrasts are localized at extranuclear lipid droplets, and two peaks at 2854 cm⁻¹ and 2925 cm⁻¹ corresponding to symmetric and asymmetric stretching vibrations of CH₂ bonds appear in the spectrum, indicating that MCR1 mainly consists of lipids. In MCR2, the MIP contrasts are localized at the nucleus and nucleolus, and the spectrum is heavily influenced by the peak attributed to CH₃, indicating that it is a component with equal contributions of CH₂ and CH₃ bonds, which can be mainly attributed to proteins. In MCR3, uniformly distributed contrasts outside the cell can be recognized, and its spectrum resembles that of OH bonds, which have an absorption peak around 3400 cm⁻¹ and monotonically increasing absorption towards higher wavenumbers in the observed wavenumber region

Fig 7  Multivariate (MCR) analysis of a MIP spectro-image of a live COS7 cell.

MIP phase change images excited at 40 different wavenumbers in the range of 2800 ~ 3250 cm⁻¹ are analyzed by the MCR method. a–c Images of each MCR component. d A phase image. e A merged image of the three MCR images. f MIR spectra of each MCR component. MCR multivariate curve resolution. sym symmetric vibrations. asym asymmetric vibrations

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The MCR1 component at 2925 cm⁻¹ (CH₂ peak) induces the MIP phase changes of 40 mrad at the lipid droplets, while the MCR2 component at 2945 cm⁻¹ (CH₃ peak) induces only 14 mrad changes in the nucleolus, and 3 mrad changes in the cytoplasm, which is calculated with the procedure shown in Methods. Since the phase noise of our QPI is ~1.1 mrad, even smaller phase changes can be detected without averaging. The estimated maximum temperature rise of this measurement is ~8 K for a lipid droplet (a sphere with a diameter of 3 µm) and ~2 K for a nucleolus (a sphere with a diameter of 5 µm), which quickly decays within ~2 and ~7 µs, respectively. These amounts of transient temperature rise have been proven to be safe for live cells

COS7 cells are cultured on a CaF₂ substrate with a thickness of 500 μm in high glucose Dulbecco's modified eagle medium with L-glutamine, phenol red, and HEPES (FUJIFILM Wako) supplemented with 10% fetal bovine serum (Cosmo Bio) and 1% penicillin-streptomycin-L-glutamine solution (FUJIFILM Wako) at 37 ℃ in 5% CO₂, and are sandwiched with another CaF2 substrate before imaging. For live-cell imaging in D₂O environment (Fig. S4), the medium is replaced by D₂O-based PBS. Note that MIP imaging with glass substrates is feasible in the spectral range observed in this work.

For Fig. 1a–d, the spherically symmetric 3-D thermal conduction equation is exploited. We use a self-made program based on the Forward Time Centered Space (FTCS) method, implemented by C programming language. We assume that the thermo-optic coefficient and heat capacity of the objects are equivalent to water because potential heat sources in cells are predominantly composed of water (~80%). We also assume that the thermo-optic coefficient does not depend on temperature. The background water absorption with a profile of ~100 μm × 100 μm is not taken into account in Fig. 1a, b because it generates a temperature change profile with a much shallower gradient compared to that of the smaller target object. We do not take into account the spatial resolution of the microscope for plotting the phase changes in Fig. 1.

For Fig. 1f, Eq. 2 is used with the boundary conditions between water and CaF₂ substrates given by

where K_water and $$K_{\mathrm{C}\mathrm{a}{\mathrm{F}}_2}$$ are the thermal conductivities of water and CaF₂, respectively. In the calculations, the thermal diffusivities and thermal conductivities of water and CaF₂ substrates are 0.146 and 2.92 µm² µs⁻¹, and 0.618 and 9.71 W m⁻¹ K⁻¹, respectively

The temporal phase noise, σ_phase, can be described as,

where σ_sensor denotes the sensor noise, v the visibility of the hologram, A_sensor and A_aperture the numbers of pixels in total and cropped areas in the spatial frequency space. The number of electrons contributing to the reconstruction of a phase image, N_electron, is calculated from the image sensor output value with sensor's parameters of full-well capacity, bit depth (2M-e⁻ sensor: 11 bit, 10k-e⁻ sensor: 16 bit), and gain (2M-e⁻ sensor: 1.73, 10k-e⁻ sensor: 1). To obtain σ_sensor, a series of images are taken without light, and the temporal standard deviation of the difference images between adjacent frames is calculated, which is converted to the number of electrons. The visibility v is evaluated by the procedure described in Supplementary Note 4. The numbers of pixels A_sensor and A_aperture are 2, 073, 600 (1440 pixels × 1440 pixels) and 47, 144 (π/4 × 245 pixels × 245 pixels) for the 2M-e⁻ sensor, and 1, 046, 529 (1023 pixels × 1023 pixels) and 31, 731 (π/4 × 201 pixels × 201 pixels) for the 10k-e⁻ sensor, respectively. Note that the reduction in the number of pixels occurred in the phase reconstruction process (A_sensor → A_aperture) results in a reduction of phase noise due to the spatial averaging effect.

A 20-μm-thick borosilicate glass capillary (VitroTubes 5002, VitroCom) is connected to a syringe via a PEEK tube (1/32 "OD × 0.02 "ID, Trajan) on one side. A droplet of D₂O-based PBS is placed on the other end of the capillary, and the liquid inside is replaced by pulling on the syringe.

The function of the curve fitting of the measured temporal data shown in Fig. 6d is written as

where h and τ denote the height of the cell and intracellular decay time, respectively. Here, the unit of height and time are μm and ms, respectively. The first and second terms represent the extracellular and intracellular temporal decay, respectively, which are linearly combined using the contribution ratio A(h). The time origin of the decay (99 ms) and the extracellular decay time (82 ms) are predetermined by a data fitting of the extracellular MIP phase change by substituting A(h) = 1. The contribution ratio A(h) is written as

where S_cell and S_water describe the MIP phase changes, which can be represented by the Lambert-Beer law as

and

where D_z is the attenuation length along the z-axis (6.73 μm at 3014 cm⁻¹

Here, the spatial distribution of the cell height h is estimated by a low-pass filtered phase image, which provides a global feature of a cell, and a literature value of refractive index difference between the inside and outside of a cell (0.0323

The velocity of water molecules passing through the cell membrane can be expressed as

with the surface area S and volume V of a cell, which can be calculated from the following equations,

and

respectively, where Δx and Δy are the lengths of a pixel in the x and y directions. The Δx and Δy are 0.44 μm in this study. The resulting values of S and V are 1404 μm² and 3779 μm³, respectively.

Prior to MCR analysis, the spatial MIP phase change contrasts reflecting the MIR beam profile are corrected by dividing the MIP phase change images of cells by normalized MIP phase change images of water without cells. Also, the wavenumber-dependent power variation of the MIR light is normalized with the data shown in Fig. 3a. MCR analysis is performed using pyMCR developed by NIST with a non-negativity constrained least-squares regressor. The spectral data with water background subtraction at the nucleolus and lipid droplets and those without water background subtraction outside the cell are used for the initial input spectra in MCR.

We calculate the MIP phase change contributed by each MCR component by the following procedure. MCR decomposes the hyperspectral data into matrices of the concentration distribution C and the pure spectra S for each MCR component i,

where x and k denote the location and the MIR wavenumber, respectively. Each component's contribution to the MIP phase change at (x, k) can be calculated as

where $$\mathrm{\Delta }\varnothing (x,k)$$ is the raw MIP phase change at (x, k).