Refraction of space-time wave packets: I. theoretical principles

Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, and isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call the "spectral curvature". Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, X wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.

Refraction of space-time wave packets: III. experiments at oblique incidence

The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibits fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence. For example, the group velocity of the refracted ST wave packet can be tuned simply by changing the angle of incidence. In the third paper, we present experimental verification of the refractive phenomena exhibited by ST wave packets at oblique incidence that were in the first paper of this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105]. We also examine a proposal for "blind synchronization," whereby identical ST wave packets arrive simultaneously at different receivers without a priori knowledge of their locations except that they are all located at the same depth beyond an interface between two media. A first proof-of-principle experimental demonstration of this effect is provided.

Refraction of space-time wave packets: II. experiments at normal incidence

The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In the first paper in this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105], we theoretically described the refraction of all families of ST wave packets at normal and oblique incidence at a planar interface between two nondispersive, homogeneous, isotropic dielectrics. Here, in this second paper in the sequence, we present experimental verification of the refractive phenomena predicted for baseband ST wave packets upon normal incidence on a planar interface. Specifically, we observe group velocity invariance, normal and anomalous refraction, and group velocity inversion leading to group delay cancellation. These phenomena are verified in a set of optical materials with refractive indices ranging from 1.38 to 1.76, including MgF₂, fused silica, BK7 glass, and sapphire. We also provide a geometrical representation of the physics associated with anomalous refraction in terms of the dynamics of the spectral support domain for ST wave packets on the surface of the light cone.

Free-space optical delay line using space-time wave packets

An optical buffer featuring a large delay-bandwidth-product-a critical component for future all-optical communications networks-remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity is continuously tunable in free space provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of  ~100 for pulses of width  ~1 ps are observed, with no fundamental limit on the system bandwidth.

What is the maximum differential group delay achievable by a space-time wave packet in free space?

The group velocity of 'space-time' wave packets - propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations - can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum - and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced 'pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.

Broadband space-time wave packets propagating 70 m

The propagation distance of a pulsed beam in free space is ultimately limited by diffraction and space-time coupling. "Space-time" (ST) wave packets are pulsed beams endowed with tight spatio-temporal spectral correlations that render them propagation-invariant. Here we explore the limits of the propagation distance for ST wave packets. Making use of a specially designed phase plate inscribed by gray-scale lithography and having a laser-damage threshold of ∼0.5  J/cm², we synthesize a ST light sheet of width ≈700  μm and bandwidth ∼20  nm, and confirm a propagation distance of ≈70  m.

Simultaneous cell traction and growth measurements using light

Characterizing the effects of force fields generated by cells on proliferation, migration and differentiation processes is challenging due to limited availability of nondestructive imaging modalities. Here, we integrate a new real-time traction stress imaging modality, Hilbert phase dynamometry (HPD), with spatial light interference microscopy (SLIM) for simultaneous monitoring of cell growth during differentiation processes. HPD uses holographic principles to extract displacement fields from chemically patterned fluorescent grid on deformable substrates. This is converted into forces by solving an elasticity inverse problem. Since HPD uses the epi-fluorescence channel of an inverted microscope, cellular behavior can be concurrently studied in transmission with SLIM. We studied the differentiation of mesenchymal stem cells (MSCs) and found that cells undergoing osteogenesis and adipogenesis exerted larger and more dynamic stresses than their precursors, with MSCs developing the smallest forces and growth rates. Thus, we develop a powerful means to study mechanotransduction during dynamic processes where the matrix provides context to guide cells toward a physiological or pathological outcome.

Meters-long propagation of diffraction-free space-time light-sheets

Space-time (ST) wave packets are pulsed beams in which the spatial frequencies and wavelengths are tightly correlated. Proper design of the functional form of these correlations results in diffraction-free and dispersion-free axial propagation; that is, propagation invariance in free space. To date, observed propagation distances of such ST wave packets has been on the order of a few centimeters. Here we synthesize an ST wave packet in the form of a pulsed optical sheet of transverse spatial width ∼200 μm and spectral bandwidth of ∼2 nm, and observe its diffraction-free propagation for approximately 6 meters. For such ST wave packets, we identify the spectral uncertainty - the precision in associating the spatial and temporal frequencies - as a critical parameter in determining the propagation-invariant distance. We present a design strategy and an experimental methodology that enables further increase in the diffraction-free length.

Phase correlation imaging of unlabeled cell dynamics

We present phase correlation imaging (PCI) as a novel approach to study cell dynamics in a spatially-resolved manner. PCI relies on quantitative phase imaging time-lapse data and, as such, functions in label-free mode, without the limitations associated with exogenous markers. The correlation time map outputted in PCI informs on the dynamics of the intracellular mass transport. Specifically, we show that PCI can extract quantitatively the diffusion coefficient map associated with live cells, as well as standard Brownian particles. Due to its high sensitivity to mass transport, PCI can be applied to studying the integrity of actin polymerization dynamics. Our results indicate that the cyto-D treatment blocking the actin polymerization has a dominant effect at the large spatial scales, in the region surrounding the cell. We found that PCI can distinguish between senescent and quiescent cells, which is extremely difficult without using specific markers currently. We anticipate that PCI will be used alongside established, fluorescence-based techniques to enable valuable new studies of cell function.

Ratiometric analysis of in vivo retinal layer thicknesses in multiple sclerosis

We performed ratiometric analysis of retinal optical coherence tomography images for the first time in multiple sclerosis (MS) patients. The ratiometric analysis identified differences in several retinal layer thickness ratios in the cohort of MS subjects without a history of optic neuritis (ON) compared to healthy control (HC) subjects, and there was no difference in standard retinal nerve fiber layer thickness (RNFLT). The difference in such ratios between HC subjects and those with mild MS-disability, without a difference in RNFLT, further suggests the possibility of using layer ratiometric analysis for detecting early retinal changes in MS. Ratiometric analysis may be useful and potentially more sensitive for detecting disease changes in MS.

Detection of retinal blood vessel changes in multiple sclerosis with optical coherence tomography

Although retinal vasculitis is common in multiple sclerosis (MS), it is not known if MS is associated with quantitative abnormalities in retinal blood vessels (BVs). Optical coherence tomography (OCT) is suitable for examining the integrity of the anterior visual pathways in MS. In this paper we have compared the size and number of retinal blood vessels in patients with MS, with and without a history of optic neuritis (ON), and control subjects from the cross-sectional retinal images from OCT. Blood vessel diameter (BVD), blood vessel number (BVN), and retinal nerve fiber layer thickness (RNFLT) were extracted from OCT images collected from around the optic nerves of 129 eyes (24 control, 24 MS + ON, 81 MS-ON) of 71 subjects. Associations between blood vessel metrics, MS diagnosis, MS disability, ON, and RNFLT were evaluated using generalized estimating equation (GEE) models. MS eyes had a lower total BVD and BVN than control eyes. The effect was more pronounced with increased MS disability, and persisted in multivariate models adjusting for RNFLT and ON history. Twenty-nine percent (29%) of MS subjects had fewer retinal blood vessels than all control subjects. MS diagnosis, disability, and ON history were not associated with average blood vessel size. The relationship between MS and lower total BVD/BVN is not accounted for by RNFLT or ON. Further study is needed to determine the relationship between OCT blood vessel metrics and qualitative retinal blood vessel abnormalities in MS.

High-Resolution Projection Microstereolithography for Patterning of Neovasculature

To gain a quantitative understanding of the way cells sense, process, and respond to dynamic environmental signals in real-time requires developing in vitro model systems that accurately replicate the 3D structure and function of native tissue. A high-resolution projection stereolithography apparatus (μSLA) capable of multimaterial and grayscale 3D patterning of cells and biomaterials at <5 μm resolution is presented. Murine cells (fibroblasts, myoblasts, endothelial, and bone marrow stromal cells) encapsulated within photosensitive hydrogels using the μSLA remain viable up to two weeks after fabrication. Harnessing the high-resolution fabrication capabilities of this machine, sub-millimeter scale angiogenic cell-encapsulating patches designed to promote targeted growth of neovasculature are printed, as assessed in vitro via enzyme-linked immunosorbent assay (ELISA) and in ovo via a chick chorioallantoic membrane assay (CAM). This application establishes the μSLA as an enabling technology that is widely adaptable to any application that requires high-resolution patterning of cells and cells signals. By providing an efficient and robust method of engineering microscale tissues with encapsulated cells, this apparatus has a range of applications including fundamental studies of extracellular matrix interactions, high throughput drug testing of physiologically relevant substitutes for native tissue, and programmable tissue engineering for applications in regenerative medicine.

Measuring the Nonuniform Evaporation Dynamics of Sprayed Sessile Microdroplets with Quantitative Phase Imaging

We demonstrate real-time quantitative phase imaging as a new optical approach for measuring the evaporation dynamics of sessile microdroplets. Quantitative phase images of various droplets were captured during evaporation. The images enabled us to generate time-resolved three-dimensional topographic profiles of droplet shape with nanometer accuracy and, without any assumptions about droplet geometry, to directly measure important physical parameters that characterize surface wetting processes. Specifically, the time-dependent variation of the droplet height, volume, contact radius, contact angle distribution along the droplet's perimeter, and mass flux density for two different surface preparations are reported. The studies clearly demonstrate three phases of evaporation reported previously: pinned, depinned, and drying modes; the studies also reveal instances of partial pinning. Finally, the apparatus is employed to investigate the cooperative evaporation of the sprayed droplets. We observe and explain the neighbor-induced reduction in evaporation rate, that is, as compared to predictions for isolated droplets. In the future, the new experimental methods should stimulate the exploration of colloidal particle dynamics on the gas-liquid-solid interface.

Spatiotemporal characterization of a fibrin clot using quantitative phase imaging

Studying the dynamics of fibrin clot formation and its morphology is an important problem in biology and has significant impact for several scientific and clinical applications. We present a label-free technique based on quantitative phase imaging to address this problem. Using quantitative phase information, we characterized fibrin polymerization in real-time and present a mathematical model describing the transition from liquid to gel state. By exploiting the inherent optical sectioning capability of our instrument, we measured the three-dimensional structure of the fibrin clot. From this data, we evaluated the fractal nature of the fibrin network and extracted the fractal dimension. Our non-invasive and speckle-free approach analyzes the clotting process without the need for external contrast agents.

Epi-illumination diffraction phase microscopy with white light

We demonstrate the first reflection-based epi-illumination diffraction phase microscope with white light (epi-wDPM). The epi-wDPM system combines the off-axis, common-path, and white light approaches, in a reflection geometry enabling sub-nanometer spatial and temporal noise levels, while providing single-shot acquisition for opaque samples. We verified the epi-wDPM results by measuring control samples with known dimensions and comparing them to measurements from other well-established techniques. We imaged gold-coated HeLa cells to illustrate the tradeoffs between epi-wDPM with low and high spatial coherence.

Diffraction phase microscopy: monitoring nanoscale dynamics in materials science [invited]

Quantitative phase imaging (QPI) utilizes the fact that the phase of an imaging field is much more sensitive than its amplitude. As fields from the source interact with the specimen, local variations in the phase front are produced, which provide structural information about the sample and can be used to reconstruct its topography with nanometer accuracy. QPI techniques do not require staining or coating of the specimen and are therefore nondestructive. Diffraction phase microscopy (DPM) combines many of the best attributes of current QPI methods; its compact configuration uses a common-path off-axis geometry which realizes the benefits of both low noise and single-shot imaging. This unique collection of features enables the DPM system to monitor, at the nanoscale, a wide variety of phenomena in their natural environments. Over the past decade, QPI techniques have become ubiquitous in biological studies and a recent effort has been made to extend QPI to materials science applications. We briefly review several recent studies which include real-time monitoring of wet etching, photochemical etching, surface wetting and evaporation, dissolution of biodegradable electronic materials, and the expansion and deformation of thin-films. We also discuss recent advances in semiconductor wafer defect detection using QPI.

Dissolution chemistry and biocompatibility of single-crystalline silicon nanomembranes and associated materials for transient electronics

Single-crystalline silicon nanomembranes (Si NMs) represent a critically important class of material for high-performance forms of electronics that are capable of complete, controlled dissolution when immersed in water and/or biofluids, sometimes referred to as a type of "transient" electronics. The results reported here include the kinetics of hydrolysis of Si NMs in biofluids and various aqueous solutions through a range of relevant pH values, ionic concentrations and temperatures, and dependence on dopant types and concentrations. In vitro and in vivo investigations of Si NMs and other transient electronic materials demonstrate biocompatibility and bioresorption, thereby suggesting potential for envisioned applications in active, biodegradable electronic implants.

Effects of spatial coherence in diffraction phase microscopy

Quantitative phase imaging systems using white light illumination can exhibit lower noise figures than laser-based systems. However, they can also suffer from object-dependent artifacts, such as halos, which prevent accurate reconstruction of the surface topography. In this work, we show that white light diffraction phase microscopy using a standard halogen lamp can produce accurate height maps of even the most challenging structures provided that there is proper spatial filtering at: 1) the condenser to ensure adequate spatial coherence and 2) the output Fourier plane to produce a uniform reference beam. We explain that these object-dependent artifacts are a high-pass filtering phenomenon, establish design guidelines to reduce the artifacts, and then apply these guidelines to eliminate the halo effect. Since a spatially incoherent source requires significant spatial filtering, the irradiance is lower and proportionally longer exposure times are needed. To circumvent this tradeoff, we demonstrate that a supercontinuum laser, due to its high radiance, can provide accurate measurements with reduced exposure times, allowing for fast dynamic measurements.

Nanoscale topography and spatial light modulator characterization using wide-field quantitative phase imaging

We demonstrate an optical technique for large field of view quantitative phase imaging of reflective samples. It relies on a common-path interferometric design, which ensures high stability without the need for active stabilization. The technique provides single-shot, full-field and robust measurement of nanoscale topography of large samples. Further, the inherent stability allows reliable measurement of the temporally varying phase retardation of the liquid crystal cells, and thus enables real-time characterization of spatial light modulators. The technique's application potential is validated through experimental results.

Digital projection photochemical etching defines gray-scale features

We demonstrate a maskless photochemical etching method that is capable of performing one-step etching of multi-level structures. This method uses a digital projector to focus an image onto the sample and define the etching pattern. By combining digital projection photochemical etching with diffraction phase microscopy, etch heights can be measured in situ in a non-destructive manner. This method is single shot, eliminating the need for expensive gray-scale masks or laser scanning methods. The etch rate is studied as a function of the wavelength and irradiance of the projected light. A lateral etch resolution of 2 μm is demonstrated by etching selected portions of the USAF-1951 target. Micropillars, multi-level plateaus, and an Archimedean spiral are etched, each in a single processing step, to illustrate the unique capabilities.

Cardiomyocyte imaging using real-time spatial light interference microscopy (SLIM)

Spatial light interference microscopy (SLIM) is a highly sensitive quantitative phase imaging method, which is capable of unprecedented structure studies in biology and beyond. In addition to the π/2 shift introduced in phase contrast between the scattered and unscattered light from the sample, 4 phase shifts are generated in SLIM, by increments of π/2 using a reflective liquid crystal phase modulator (LCPM). As 4 phase shifted images are required to produce a quantitative phase image, the switching speed of the LCPM and the acquisition rate of the camera limit the acquisition rate and, thus, SLIM's applicability to highly dynamic samples. In this paper we present a fast SLIM setup which can image at a maximum rate of 50 frames per second and provide in real-time quantitative phase images at 50/4 = 12.5 frames per second. We use a fast LCPM for phase shifting and a fast scientific-grade complementary metal oxide semiconductor (sCMOS) camera (Andor) for imaging. We present the dispersion relation, i.e. decay rate vs. spatial mode, associated with dynamic beating cardiomyocyte cells from the quantitative phase images obtained with the real-time SLIM system.

Fourier phase microscopy with white light

Laser-based Fourier phase microscopy (FPM) works on the principle of decomposition of an image field in two spatial components that can be controllably shifted in phase with respect to each other. However, due to the coherent illumination, the contrast in phase images is degraded by speckles. In this paper we present FPM with spatially coherent white light (wFPM), which offers high spatial phase sensitivity due to the low temporal coherence and high temporal phase stability due to common path geometry. Further, by using a fast spatial light modulator (SLM) and a fast scientific-grade complementary metal oxide semiconductor (sCMOS) camera, we report imaging at a maximum rate of 12.5 quantitative phase frames per second with 5.5 mega pixels image size. We illustrate the utility of wFPM as a contrast enhancement as well as dynamic phase measurement method by imaging section of benign colonic glands and red blood cell membrane fluctuation.

Spectroscopic diffraction phase microscopy

We present spectroscopic diffraction phase microscopy (sDPM) as a method capable of measuring quantitative phase images at multiple wavelengths. sDPM uses a spatial light modulator at the Fourier plane of a lens to select desired wavelengths from the white light illumination of a grating. The quantitative phase information at different wavelengths allows us to decouple the refractive index and the thickness from the phase shift induced by biological cells. We demonstrate the capability of the setup by dispersion measurements of microsphere beads and RBCs.

Derivative method for phase retrieval in off-axis quantitative phase imaging

We present a method for phase retrieval in off-axis interferometric systems. By numerically calculating the transverse 1st and 2nd order derivatives of the interferogram, we show that one can directly retrieve the quantitative phase image, without the need for Fourier or Hilbert transformations. Because of this, the method is significantly faster than the current approaches. We illustrate our method using biological specimen data from three different off-axis quantitative phase imaging techniques.

Diffraction phase microscopy with white light

We present white light diffraction phase microscopy (wDPM) as a quantitative phase imaging method that combines the single shot measurement benefit associated with off-axis methods, high temporal phase stability associated with common path geometries, and high spatial phase sensitivity due to the white light illumination. We propose a spatiotemporal filtering method that pushes the limit of the pathlength sensitivity to the subangstrom level at practical spatial and temporal bandwidths. We illustrate the utility of wDPM with measurements on red blood cell morphology and HeLa cell growth over 18 hours.

Translational and rotational coupling in Brownian rods near a solid surface

An anisotropic macromolecule confined between two surfaces displays Brownian motion predominantly in the plane parallel to these surfaces. It can be expected that both the rotational and translational diffusion coefficients are strongly affected by hydrodynamic interactions with the walls. This work studies the more extreme case in which a rodlike particle comes into contact with a wall or in very close proximity (order of 100 nm). Experimental data have been gathered and analyzed demonstrating the rod tethering on a surface. This is compared with numerical simulations to allow estimates of proximity to the surface. The experimental data show that particle tethered motion is subject to varied degrees of constraining which imply subtle deviations in the Brownian dynamical behavior. The key finding is that a rotational-translational coupling occurs which is markedly different from the translational and rotational movements normally predicted for anisotropic macromolecules.

Simultaneous measurement of translation and tilt using digital speckle photography

A Michelson-type digital speckle photographic system has been proposed in which one light beam produces a Fourier transform and another beam produces an image at a recording plane, without interfering between themselves. Because the optical Fourier transform is insensitive to translation and the imaging technique is insensitive to tilt, the proposed system is able to simultaneously and independently determine both surface tilt and translation by two separate recordings, one before and another after the surface motion, without the need to obtain solutions for simultaneous equations. Experimental results are presented to verify the theoretical analysis.

Motion detection using extended fractional Fourier transform and digital speckle photography

Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

Simultaneous measurement of out-of-plane displacement and slope using a multiaperture DSPI system and fast Fourier transform

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second after loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center.

Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS)

Digital speckle pattern interferometry (DSPI) and digital shearography (DS) are well known optical tools for qualitative as well as quantitative measurements of displacement components and its derivatives of engineering structures subjected either static or dynamic load. Spatial phase shifting (SPS) technique is useful for extracting quantitative displacement data from the system with only two frames. Optical configurations for DSPI and DS with a double aperture mask in front of the imaging lens for spatial phase shifting are proposed in this paper for the measurement of out-of-plane displacement and its first order derivative (slope) respectively. An error compensating four-phase step algorithm is used for quantitative fringe analysis.

Assessing Watershed-Scale, Long-Term Hydrologic Impacts of Land-Use Change Using a GIS-NPS Model

Land-use change, dominated by an increase in urban/impervious areas, has a significant impact on water resources. This includes impacts on nonpoint source (NPS) pollution, which is the leading cause of degraded water quality in the United States. Traditional hydrologic models focus on estimating peak discharges and NPS pollution from high-magnitude, episodic storms and successfully address short-term, local-scale surface water management issues. However, runoff from small, low-frequency storms dominates long-term hydrologic impacts, and existing hydrologic models are usually of limited use in assessing the long-term impacts of land-use change. A long-term hydrologic impact assessment (L-THIA) model has been developed using the curve number (CN) method. Long-term climatic records are used in combination with soils and land-use information to calculate average annual runoff and NPS pollution at a watershed scale. The model is linked to a geographic information system (GIS) for convenient generation and management of model input and output data, and advanced visualization of model results.The L-THIA/NPS GIS model was applied to the Little Eagle Creek (LEC) watershed near Indianapolis, Indiana, USA. Historical land-use scenarios for 1973, 1984, and 1991 were analyzed to track land-use change in the watershed and to assess impacts on annual average runoff and NPS pollution from the watershed and its five subbasins. For the entire watershed between 1973 and 1991, an 18% increase in urban or impervious areas resulted in an estimated 80% increase in annual average runoff volume and estimated increases of more than 50% in annual average loads for lead, copper, and zinc. Estimated nutrient (nitrogen and phosphorus) loads decreased by 15% mainly because of loss of agricultural areas. The L-THIA/NPS GIS model is a powerful tool for identifying environmentally sensitive areas in terms of NPS pollution potential and for evaluating alternative land use scenarios for NPS pollution management.