<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-K

/X/   ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
      EXCHANGE ACT OF 1934 [FEE REQUIRED]

      FOR THE FISCAL YEAR ENDED MARCH 31, 1998
                                      OR
/ /   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
      EXCHANGE ACT OF 1934

                          Commission file number 1-6549

                     AMERICAN SCIENCE AND ENGINEERING, INC.
             (Exact name of registrant as specified in its charter)

MASSACHUSETTS                                           04-2240991
(State or other jurisdiction of            (I.R.S. Employer Identification No.)
incorporation or organization)

829 MIDDLESEX TURNPIKE, BILLERICA, MASSACHUSETTS            01821
(Address of principal executive offices)                  (Zip Code)

Registrant's telephone number, including area code (978) 262-8700

Securities registered pursuant to Section 12(b) of the Act:

<TABLE>
<CAPTION>
Title of each class                   Name of each exchange on which registered
-------------------                   -----------------------------------------
<S>                                   <C>
Common Stock ($.66 2/3 par value)     American Stock Exchange
</TABLE>

Securities registered pursuant to Section 12(g) of the Act:  None

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.  YES /X/   NO / /

Indicate by check mark if disclosure of delinquent filers pursuant to Item 405
of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10- K or any amendment to
this Form 10-K.     /X/

The aggregate market value of voting stock held by non-affiliates of the
registrant on June 30, 1998 was $67,776,063

4,780,202 shares of Registrant's Common Stock were outstanding on June 30, 1998.

                     The Exhibit Index is located on page 47
                               PAGE 1 OF 75 PAGES
<PAGE>   2
PART I

ITEM 1.   BUSINESS

American Science and Engineering, Inc., a Massachusetts corporation formed in
1958 (together with its subsidiary, the "Company"), develops, produces, markets,
sells and provides research and engineering services with respect to X-ray
inspection systems.

-  X-RAY PRODUCTS

The Company provides a full line of X-ray detection and imaging products used
primarily for the detection of illegal drugs, terrorist explosives, and smuggled
goods. This equipment is purchased by sophisticated government and commercial
clients who place a premium on the detection of organic material in complex
backgrounds and the ability to see the contents of containers with precision.
The Company utilizes proprietary transmission and backscatter X-ray detection to
provide differentiation of bombs, drugs and contraband in camouflaged
environments. The range of application includes border control and manifest
verification, protection of high risk government offices, mail and parcel
screening, correctional facility security, military security, executive
security, aviation security, and special event security (e.g. Olympics, UN 50th
Anniversary and World Cup Soccer). The Company's market is driven by domestic
and global trends toward increasing use of terrorism for political purposes; the
continued global proliferation of drug smuggling; and the continuing increase in
global trade which creates greater incentives and opportunities to evade duties
by misdeclaring manifests.

The surge in cross border drug smuggling has created a requirement for cargo and
vehicle inspection. With the assistance of the U.S. Department of Defense and
U.S. Customs, the Company has developed the CargoSearch(TM) line of X-ray
inspection equipment. Based on the success of the fixed-site CargoSearch(TM)
prototype at Otay Mesa, CA, an additional four fixed-site systems are now on
line for U.S. Customs to inspect trucks for hidden drugs on the Mexican border
and three additional installations are expected to be completed along the border
over the next 9 months. The CargoSearch(TM) product family includes fixed site
inspection for trucks and containers; mobile equipment to inspect trucks,
containers and cars; and a fixed pallet inspection system. This equipment has
further application for the detection of weapons and explosives for border
security and protection of high risk facilities. In addition, there is an
emerging application for manifest verification for export and import cargoes at
ports and other border crossings. The Company has announced the sale of several
CargoSearch(TM) systems to be delivered over the next three years for a variety
of applications overseas, including a South African port for manifest
verification and drug smuggling; a border crossing in Abu Dhabi primarily for
weapons detection; and several systems in Egypt for manifest verification and
other anti-smuggling applications at ports.

The Company offers high performance X-ray inspection systems at prices that have
generally been higher than those of competing, less capable systems. However, in
recent years, the Company has brought to the marketplace several new products
that are priced significantly lower than competing systems. Across the entire
range of its X-ray inspection systems, the Company has focused on selling
products with unique features that create strong product differentiation and
competitive advantage.


                                       2
<PAGE>   3
The Company's product line currently includes 12 models. These models can be
broadly categorized into 4 groups including: the Model 101 series, the Model 66
series, the CargoSearch(TM) family and the BodySearch(TM) Personnel Inspection
System. All of these systems utilize the Company's Z(R) Backscatter technology
(aspects of which are covered by issued and pending U.S. patents), which detects
organic materials, such as illegal drugs, plastic explosives and plastic
weapons, even when they are undetected by other competing systems.

The Micro-Dose(R) Model 101 Series consists of 6 models. The mobile Model
101VAN(TM) is a sophisticated, vehicle mounted inspection system designed and
built to the rigorous specifications of the U.S. Customs Service. The Model
101ZZ(R) Trailer is a field deployable system for extended on site security
details. The Models 101Z(R), 101ZZ(R), 101GT(TM), and 101XL(TM) are moveable
(but not mobile), conveyor based systems allowing rapid inspection of high
volumes of luggage and other packages.

The Model 66(R) handles small packages using the patented Z(R) Backscatter
technology. This technology was validated by a study conducted by several U.S.
government agencies involving the Model 66(R) and competitive systems in which
the Model 66(R) was determined to have superior detection capability for
terrorist devices hidden in complex backgrounds. This test resulted in increased
order demand from both government and commercial clients, including a number of
Fortune 100 companies.

The CargoSearch(TM) family of products includes the CargoSearch(TM) system, the
relocatable IsoSearch(TM) system, MobileSearch(TM) system, and the
PalletSearch(TM) system. The CargoSearch(TM) system is a non-intrusive
inspection technology for the X-ray scanning of trucks, cars, cargo containers,
pallets, and air cargo using the Company's unique and patented Z(R) Backscatter
technology. The fixed CargoSearch(TM) system sells for a turnkey price
substantially lower than competing systems. The first CargoSearch(TM) system has
been operating at the U.S. Customs facility in Otay Mesa, California, the
busiest truck border crossing in the United States and was recently joined by
four other systems in Texas and California. U.S. Customs has ordered three
additional CargoSearch(TM) systems to be installed along the border with Mexico.

The first MobileSearch(TM) system was delivered under a $1.8 million contract
with the Defense Advanced Research Project Agency (DARPA). This mobile version
of a CargoSearch(TM) system is a self-contained unit inside a conventional truck
which is deployable within minutes and provides the transport mechanism via a
hydraulic drive. The Company is marketing the MobileSearch(TM) system to
agencies of the U.S. government and to foreign security and customs agencies.
The Company has delivered a second system to the U.S. government and has
received orders for a number of additional units from the U.S. government and
two foreign governments. All of the units after the first include both Z(R)
Backscatter and transmission X-ray capabilities.

PalletSearch(TM) was designed for the inspection of pallets for the detection of
contraband, weapons and explosives for high security facilities where high
confidence inspection is a requirement. The first PalletSearch(TM) system was
delivered during fiscal 1997 to an ultra-secure agency of the U.S. government,
and additional units have been ordered by a foreign government for customs
inspection applications.


                                        3
<PAGE>   4
The BodySearch(TM) Personnel Inspection System offers a fast, safe, and
non-intrusive way to screen individuals for the detection of concealed weapons,
drugs, and illegal contraband. This system is used for drug detection and head
of state security as well as for correctional facility security. The Company
sold one unit during fiscal 1998 to a state prison.

The Company has patents in the United States, Germany, Japan, and The United
Kingdom, as well as five (5) patents pending under the Patent Cooperation
Treaty, none of which have reached the national phase requiring the
identification of specific countries in which patents will be sought. The
Company has sold product in, or has sales activity in most major regions of the
world including Africa, Asia, Europe, the Middle East and South America. Each
U.S. patent issued prior to June 1995 has a duration of the longer of seventeen
years from the date of issue or twenty years from the date of application; U.S.
and virtually all foreign patents issued after May 1995 will have a duration of
twenty years from the date of application. The Company relies on certain
proprietary technology and know-how, as well as certain of these patents, to
establish and maintain its competitive position. The Company believes that its
patents, proprietary technology and know-how provide substantial protection for
the Company's competitive position and the Company has publicly stated its
intent to aggressively protect its intellectual property assets, by litigation
or other means, as appropriate.

The Company's X-ray products are marketed to private and governmental
organizations through a sales force that contacts potential customers. This
sales force includes Company personnel based in the United States as well as
representatives under contracts to sell in foreign countries who are generally
on a commission basis.

Most Micro-Dose(R) Systems are built for existing orders, and the Company
maintains an inventory of common parts and sub-assemblies for the systems in
order to meet expected customer delivery requirements.

The Company is heavily dependent upon sales to agencies of the U.S. Government,
and reductions or delays in procurements of the Company's systems by these
agencies may have a material adverse effect on the Company. Sales to U.S.
Government agencies, in general, are generated by responding to a "Request for
Quote" and are subject to standard and routine U.S. Government pre and post
contract award audit as well as review of the Company's compliance with the
Federal Acquisition Regulations. During fiscal 1998, the majority of sales of
X-ray products were under (i) direct contracts with the U.S. Government, and
(ii) subcontracts with prime contractors working under direct contracts with the
U.S. Government. Some of the Company's contracts with the government are on a
cost reimbursement basis, including provisions preventing final billing until
completion of the contract, and virtually all are cancelable at the government's
discretion. The Company has not experienced any material losses as the result of
such contractual provisions.

The U.S. Customs Service is a major customer (with sales of more than 36 percent
of the Company's consolidated revenues in fiscal 1998). The loss of this
customer would be likely to have a material adverse effect on the Company taken
as a whole. The Company believes that it has a satisfactory relationship with
the U.S. Customs Service. The Company has stated its intent to reduce its
reliance on sales to the U.S. government, and during and after the end of fiscal
1998, the Company announced several sales to agencies of foreign governments
totaling over $45 million for delivery over three years.


                                       4
<PAGE>   5
The Company has many competitors in the X-ray product market, including several
large and well established manufacturers of security X-ray equipment with
financial and other resources greater than those of the Company. Certain X-ray
security system customers select such systems based largely on price. Other
customers, notably the U.S. Government and users in countries with high levels
of concern over security, tend to select systems based largely on performance
and detection capability. The Company's systems offer premium performance and
have in the past, with the exception of CargoSearch(TM), generally been priced
higher than many competing systems. The Company believes that its patented and
proprietary technology give it a strong competitive position in the sale of
security systems to customers concerned with performance and detection. The
Company also believes that its strategy of concentrating on products with unique
features and/or competitive pricing will give it a strong position to increase
its sales of X-ray systems.

The Company has not experienced during the last year, and does not currently
anticipate, any hardware delivery delays due to raw material shortages. Most
procured material is from U.S. sources. However, the Company is dependent on
certain overseas sole source providers of important components. No rare or
exotic materials are utilized.

The Company complies with applicable Health and Human Services regulations
outlined under the "Regulations for the Administration and Enforcement of the
Radiation Control for Health and Safety Act of 1968" (21CFR 1020.40), published
by the U.S. Department of Health and Human Services. All X-ray products of the
Company comply with all applicable U.S. Government regulatory standards.


-  RESEARCH AND DEVELOPMENT

The Company conducted approximately $2,785,000 of government sponsored research
primarily focused on technologies for the detection of illicit drugs,
explosives, and other security issues in fiscal 1998. This compares to
$2,278,000 and $2,750,000 of government sponsored research and development in
fiscal 1997 and 1996, respectively. In addition, the Company spent approximately
$2,856,000 of its own funds for research relating to the development of new
products or services during fiscal 1998, compared to $1,602,000 and $533,000 in
fiscal 1997 and 1996, respectively.

A significant amount of the Company's research and development work is obtained
via contracts or subcontracts that typically provide for reimbursement of
allowable costs plus a fixed fee. The Company's contracts in these areas are
obtained by submitting research and development proposals to various
organizations, sometimes in response to requests for such proposals. The
Company's contract research ranges from advances in X-ray systems and image
analysis to integrated system development for niche security inspection
problems.

-  PERSONNEL

As of March 31, 1998 the Company had 198 employees compared to 167 employees at
the end of the prior year. All Company employees sign nondisclosure agreements
as a condition of employment.



                                       5
<PAGE>   6
-  SALES BACKLOG

The Company's firm sales backlog was $ 17,299,000 at March 31, 1998 and
$15,584,000 at March 28, 1997.

A majority of the Company's contracts with the U.S. Government contain clauses
permitting the government to terminate the contract for convenience upon certain
terms and conditions, including payment to the Company of an appropriate fee or
profit on work performed. The total of such contracts in the backlog was
$11,053,000 at the end of fiscal year 1998 and $11,220,000 at the end of fiscal
year 1997. It is estimated that approximately 89% of the 1998 backlog will be
filled within the fiscal year ending March 31, 1999.

Subsequent to March 31, 1998, the Company received an order from the Customs
Authority of the Arab Republic of Egypt for ten CargoSearch systems with a
contract value of $35,000,000. The systems are to be delivered over the next 36
months. This order is not included in the Company's firm backlog reported at
March 31, 1998.

-  FINANCIAL INFORMATION ABOUT FOREIGN AND DOMESTIC OPERATIONS AND EXPORT SALES

All export sales are made in U.S. dollars, and many non-U.S. Government export
sales are either secured by irrevocable letters of credit or paid in advance.
Export sales are believed by the Company to have been at least as profitable as
similar domestic sales. All of the Company's assets and operations are
maintained in the United States. The Company has not encountered, and does not
anticipate encountering, risks attendant to export sales that are greater than
risks attendant to domestic sales. The following chart provides information
about the breakdown between domestic and export sales for the indicated fiscal
years.

Net Sales and Contract Revenues (Dollars in thousands)


<TABLE>
<CAPTION>
                                              1998             1997             1996
                                         ---------        ---------        ---------
<S>                                      <C>              <C>              <C>
Domestic                                 $  26,799        $  23,703        $  14,526
Export                                       5,900            4,776            3,289
Percent of Export Revenue by Major
Region:
    Middle East and Africa                    59.7%            22.2%            20.9%
    Pacific Rim                               28.3             60.9             39.2
    Europe                                     8.9              4.4             34.4
    All Other                                  3.1             12.5              5.5
</TABLE>

ITEM 2.   PROPERTIES

In March of 1995, the Company took advantage of substantial cost savings
opportunities presented by a soft market for R&D space in the Greater Boston
area and moved its operations to Billerica, Massachusetts, approximately 20
miles outside of Boston. The move has provided the Company with more efficient
manufacturing and laboratory space and, in the first year,


                                       6
<PAGE>   7
saved the Company approximately $1,100,000 in occupancy costs as compared to the
previous lease while providing room for future growth.

The Company's executive offices and its research, manufacturing and warehouse
facilities are now located in 118,300 square feet of space in a 160,000 square
foot single-story, concrete and brick building owned by an unaffiliated real
estate limited partnership. The remaining space in the building is currently
leased by the owner to an unaffiliated manufacturing company. The Company
occupies the space under a long-term lease with a ten year initial term that
commenced March 1, 1995, and one (1) ten year optional extension term. In
January 1998, the Company leased 12,700 square feet of additional manufacturing
and office space. This lease has a term of five years. The facilities are
currently fully utilized on a one-shift basis. The Company can add additional
capacity by adding second and third shifts if necessary.

ITEM 3.   LEGAL PROCEEDINGS

In May 1996, Vivid Technologies, Inc., filed a civil action in the United States
District Court for the District of Massachusetts against the Company, seeking
inter alia a declaratory judgment that Vivid had not infringed upon certain of
the Company's patents relating to backscatter. On May 12, 1997, Vivid filed a
proposed Amended Complaint narrowing its claim and seeking inter alia a
declaratory judgment that Vivid had not infringed on two claims on AS&E United
States Patent number 5,253,283, entitled "Inspection Method and Apparatus with
Single Color Pixel Imaging." On January 28, 1998, the Court granted Vivid's
request for a declaratory judgement. The Company has appealed the judgment and
the case is proceeding in the United States Court of Appeals for the Federal
Circuit. Due to certain rulings made by the District Court, the Company was
unable to obtain certain discovery the Company believes is essential to
determine whether Vivid is infringing on the '283 patent. Through the appeal
process, the Company is pursuing its request for discovery, and, if successful,
expects to pursue an infringement action against Vivid to the extent consistent
with the evidence discovered.

ITEM 4.   SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

No matter was submitted to a vote of the Company's security holders during the
fourth quarter of the fiscal year covered by this report.


                                       7
<PAGE>   8
PART II

ITEM 5. MARKET FOR THE COMPANY'S COMMON EQUITY AND RELATED STOCKHOLDER MATTERS

The Company's Common Stock is listed on the American Stock Exchange (ticker
symbol ASE). The market price range for the Common Stock for the last two fiscal
years follows:

<TABLE>
<CAPTION>
Fiscal Year      Quarter Ended           High         Low
-----------      -------------           ----         ---
<S>              <C>                     <C>          <C>
1998             March 31, 1998          14 3/4       11 1/4
                 December 31, 1997       14 1/2       10     
                 September 30, 1997      13 3/8       9 1/4
                 June 27, 1997           12 1/4       9 5/8

1997             March 28, 1997          14 7/8       12 1/8
                 December 27, 1996       16 3/4       9 7/8
                 September 27, 1996      18 3/4       9 3/8
                 June 28, 1996           12 1/4       8 3/4
</TABLE>

As of June 30, 1998, there were approximately 1,478 holders of record of the
Company's Common Stock.

No cash dividends have been declared in the two most recent fiscal years and the
Board of Directors does not contemplate paying any dividends in the immediate
future.

The Company's credit facility restricts the payment of dividends (except in
shares of the Company's stock) without consent of the bank.

ITEM 6.   SELECTED FINANCIAL DATA

(Dollars in thousands, except per share amounts)

<TABLE>
<CAPTION>
Fiscal year                   1998          1997          1996           1995            1994
                            -------       -------       -------       --------        --------
<S>                         <C>           <C>           <C>           <C>             <C>
Net sales and contract
revenues                    $32,699       $28,479       $17,815       $ 12,997        $ 11,182

Net income (loss)             4,661         1,925           802           (967)         (3,335)

Income (loss) per
share-diluted                   .95           .40           .18           (.23)           (.83)

Total assets                 25,993        15,514        14,295         10,734          10,541

Obligations under
capital leases                   42            60            75            233             251

Stockholders'
investment                   16,084        10,150         7,501          5,592           6,294

Book value per share           3.39          2.21          1.67           1.31            1.52
</TABLE>


                                       8
<PAGE>   9
ITEM 7. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS

-     1998 COMPARED TO 1997

-     OVERVIEW

Net sales and contract revenues for fiscal 1998 improved by 15% to $32,699,000
versus fiscal 1997 net sales of $28,479,000. The Company's income before taxes
of $2,698,000, an increase of 35% compared to a $2,003,000 income before taxes
in the previous year. During fiscal 1998, the Company recorded a net tax benefit
associated with net operating loss carryforwards and other tax items of
$1,963,000. Net income for fiscal 1998 was $4,661,000 ($.95 per share, on a
diluted basis) as compared to $1,925,000 ($.40 per share, on a diluted basis) in
fiscal 1997. Backlog at March 31, 1998 was $17,299,000, an 11% increase over the
backlog reported at previous fiscal year end.

CHANGES IN FINANCIAL CONDITION - Cash and cash equivalents at year end decreased
by $912,000 to $2,290,000, compared to $3,202,000 in 1997. Accounts receivable
and unbilled costs and fees increased by $2,070,000 and $2,409,000 respectively
from the prior year due to the increased shipments made during 1998 and
performance on several contracts. Inventories increased by $4,151,000 during
1998 to support the growth in X-ray equipment shipments and backlog. Customer
deposits increased $1,151,000 due to the advanced payment from a certain
long-term contract. Deferred income taxes increased $2,556,000 as a result of
the Company recording a tax benefit associated with its net-operating loss
carryforwards and other tax assets.

RESULTS OF OPERATIONS - Net sales and contract revenues increased by $4,220,000
or 15% during fiscal year 1998. In 1998, security systems and field service
revenues of $29,914,000 increased by $3,713,000 or 14%. Contract research and
engineering revenues of $2,785,000 increased by $507,000 or 22%.

Cost of sales and contracts in 1998 of $19,816,000 was $1,393,000 higher than
the previous year primarily due to increased equipment sales and performance on
several contracts. Cost of sales and contracts represented 61% of revenues
during 1998, compared to 65% in 1997. This decline in the cost of sales ratio
was due to a more profitable product mix and a larger revenue base over which to
spread fixed costs in 1998.

Selling, general and administrative expenses of $7,425,000 were $931,000 higher
than the previous year and represented 23% of revenues, unchanged from 1997. The
increased spending level was primarily due to expanded international sales and
marketing activities and costs associated with recruiting for the Company's
expanded staff requirements.

Company funded research and development spending increased to $2,856,000 in
1998, a 78% increase compared to the $1,602,000 in spending in 1997. Research
and development spending in fiscal 1998 and fiscal 1997 was 9% and 6% of
revenues, respectively.

In the fourth quarter of fiscal 1998, the Company recorded a tax benefit
associated with net operating loss carryforwards and other tax assets as
explained in Footnote 5 to the Financial Statements. The aggregate tax benefit
recognized was $2,072,000 which resulted in a net tax benefit for the year of
$1,963,000. In fiscal 1997, the Company recorded a provision for income taxes of
3.9%, of which the significant components included alternative minimum tax
payable to the federal government and amounts for state income taxes.


                                       9
<PAGE>   10
The Company recorded net profits of $4,661,000 for fiscal year 1998, an
improvement of $2,736,000, or 142%, over net income of $1,925,000 in the
previous year. Using fiscal 1997 tax provision rates, fiscal 1998 net profits
would have been $2,589,000, representing an increase of 34% over fiscal 1997.
The Company was profitable in all quarters.

LIQUIDITY AND CAPITAL RESOURCES - Net cash used for operating activities was
$696,000, compared to $158,000 net cash provided by operating activities in
1997. During 1998, the Company received $884,000 from the exercise of stock
options. Cash and cash equivalents at March 31, 1998 stood at $2,290,000, a
decrease of $912,000 over the prior year end. Working capital at the end of 1998
increased 49% to $14,691,000. The Company's current ratio decreased to 2.6 as
compared to 3.3 at the end of 1997.

Fiscal 1998 capital expenditures totaled $1,082,000. This was an increase of
48%, or $352,000, from the prior year capital expenditures of $730,000. Capital
expenditures were comprised primarily of investments in information technology,
leasehold improvements, and furniture and fixtures. Capital expenditures are
funded by cash generated by operations or from the lines of credit available to
the Company.

At the end of fiscal 1998, the Company had $8.0 million in approved bank lines
of credit to be used either for short term cash borrowings to support working
capital growth or standby letters of credit to support the bonding requirements
of foreign contracts. At the end of fiscal 1998, no cash borrowings were
outstanding and $1.2 million in standby letters of credit were in effect against
this credit facility. During April 1998, the Company renegotiated the line of
credit, from $8.0 million to $12.0 million in anticipation of the increased
standby letter of credit capacity required to support the growth in
international orders. The Company's credit facility restricts the payment of
dividends, except in shares of the Company's stock, without consent of the bank.

Given the Company's receipt of various international contract awards over the
previous 90 days totaling $45 million, management believes that additional
credit facilities will be necessary for expanded standby letter of credit
capacity to support foreign equipment sales. Management is currently in the
process of negotiating with two commercial banks and the U.S. Export Import Bank
to increase its bank lines of credit and anticipates having a new credit
facility in place during the second quarter of fiscal year 1999.

MANAGEMENT ACTIONS - During fiscal 1998 AS&E achieved several milestones
associated with receipt of new orders, further progress toward the
commercialization of the Company's CargoSearch(TM) family of products, and
continued expansion of the Company's domestic and international customer base.
Examples include the following:


-     During the third quarter of fiscal year 1998, the Company delivered its
      second MobileSearch(TM) system under a $2.7 million contract. Work began
      under a $3.8 million contract received from the U.S. Department of
      Defense-Counterdrug Technology Development Program for two additional
      enhanced MobileSearch(TM) systems.

-     Throughout the fiscal year the Company improved its position significantly
      in the international market. In March 1998 the Company received an order
      from Portnet, the Port Authority in South Africa, for a new unique version
      of AS&E's CargoSearch(TM) system. The system, called IsoSearch(TM),
      combines features of both fixed-site and mobile systems
      currently sold by the Company and will allow Portnet to relocate the
      system within or between ports.


                                       10
<PAGE>   11
-     Subsequent to year end the Company received a MobileSearch(TM) order from
      a Middle Eastern customer for counter terrorism; as well as an $8.8
      million dollar order from the Abu Dhabi United Arab Emirates Customs
      Department for a fixed-site CargoSearch(TM) for truck inspection on the
      border with Saudi Arabia. The Company also received a $35 million order
      from the Customs Authority of the Arab Republic of Egypt for ten of the
      Company's CargoSearch(TM) family of products, including multiple units of
      each of the fixed-site CargoSearch(TM), MobileSearch(TM) and
      PalletSearch(TM) systems.


The Company has developed a plan to ensure its systems are compliant with the
requirements to process transactions in the year 2000. The Company is currently
in the process of testing the compliance of the internal information systems.
The Company has also commenced the process of assessing its external systems and
software, by sending vendor notifications and questionnaires, to determine
whether or not they are year 2000 compliant. Spending for compliance maintenance
and modifications has been expensed as incurred. Management does not expect
remediation costs of year 2000 to be material. Any new hardware and software has
been capitalized, and will be depreciated or amortized over the useful life of
the asset acquired. Management does not believe these changes will have any
material effect on ongoing results of operations.

-     1997 COMPARED TO 1996

-     OVERVIEW

Net sales and contract revenues for fiscal 1997 improved by 60% to $28,479,000
versus fiscal 1996 net sales of $17,815,000. The Company earned operating
profits of $1,925,000 (.40 per share, on a diluted basis), an increase of 140%
compared to a $802,000 profit (.18 per share, on a diluted basis) in the
previous year. Backlog at March 28, 1997 was $15,584,000, a 28% increase over
the backlog reported at previous fiscal year end.

CHANGES IN FINANCIAL CONDITION - Cash and cash equivalents at year end decreased
by $175,000 to $3,202,000, compared to $3,377,000 in 1996. However, in contrast
with the previous year end, almost no customer deposits were held at the end of
fiscal year 1997 that would serve to offset the reported cash and cash
equivalent position. Accounts receivable increased by $1,323,000 from the prior
year due to the increased shipments made during 1997. Inventories increased by
$422,000 during 1997 to support the growth in X-ray equipment shipments and
backlog. Customer deposits decreased $2,670,000 due to the attainment of
milestones against certain long-term contracts. Current and noncurrent deferred
revenue, in total, increased by $811,000 from the previous year as a result of
advanced payments for extended warranty and service contracts.

RESULTS OF OPERATIONS - Net sales and contract revenues increased by $10,664,000
or 60% during fiscal year 1997. In 1997, security systems and field service
revenues of $26,201,000 increased by $11,136,000 or 74%. Contract research and
engineering revenues of $2,278,000 decreased by $472,000 or 17%.

Cost of sales and contracts in 1997 of $18,423,000 was higher than the previous
year primarily due to increased equipment sales. Cost of sales and contracts
represented 65% of revenues during 1997, compared to 66% in 1996. This decline
in the cost of sales ratio was due to a larger revenue base over which to spread
fixed costs in 1997.

Selling, general and administrative expenses of $6,494,000 were $1,906,000
higher than the previous year and represented 23% of revenues, compared to 26%
in 1996. The increased spending level was primarily due to expanded sales and
marketing activities, costs associated with the Company's policy of aggressively
defending its intellectual property rights, and the costs associated with
recruiting for the


                                       11
<PAGE>   12
Company's expanded management and staff requirements. The improvement in the
ratio of SG&A expenses to revenues is a result of the increased sales volume.

Company funded research and development spending increased to $1,602,000 in
1997, a 200% increase compared to the $533,000 in spending in 1996. In
accordance with accounting conventions, development costs in excess of contract
amounts are included in the cost of sales for certain customer funded research
contracts.

The Company's net profit of $1,925,000 for fiscal year 1997 represents an
improvement of $1,123,000, or 140%, over net income of $802,000 in the previous
year. The Company was profitable in all quarters, and profits increased in each
quarter during fiscal year 1997.

LIQUIDITY AND CAPITAL RESOURCES - Corporate liquidity and capital resources
improved during fiscal year 1997. Net cash provided by operating activities was
$158,000, compared to $1,966,000 net cash provided by operating activities in
1996. Additionally, during 1997, the Company received $412,000 from the exercise
of stock options. Cash and cash equivalents at March 28, 1997 stood at
$3,202,000, a decrease of $175,000 over the prior year end. Customer deposits
decreased by $2,670,000 compared to 1996, resulting in an improvement in
liquidity despite the Company's slightly lower cash and investments. Working
capital at the end of 1997 increased 45% to $9,856,000. The Company's current
ratio also increased to 3.3 as compared to 2.0 at the end of 1996.

At the end of fiscal 1997, the Company had $2.5 million in approved bank lines
of credit against which there were no borrowings.

Given the Company's current cash position and access to unused borrowing
capacity, management believes that sufficient capital resources are in place to
support the Company's operations over the next several quarters.

MANAGEMENT ACTIONS - During fiscal 1997 AS&E achieved several milestones
associated with receipt of new orders, further progress toward the
commercialization of the Company's CargoSearch(TM) family of products, and
continued expansion of the Company's domestic and international customer base.
Examples include the following:

-     In March 1997 the Company received orders totaling $8.5 million from U.S.
      Customs for the installation of four fixed-site CargoSearch(TM) systems
      for truck inspection along the Southwest border, bringing the total of
      such orders to eight. Two systems have been successfully installed and are
      currently operational.

-     The first PalletSearch(TM) system for inspection of high security freight
      and cargo was successfully installed in September 1996 at an ultra-secure
      U.S. agency in Washington, D.C.

-     The Company's first MobileSearch(TM) system, delivered in January 1996,
      has demonstrated its value as an enforcement tool and is now patrolling a
      500 mile stretch of the Mexican border. In July 1996 the Company received
      a $2.7 million order from the department of Defense Advanced Research
      Projects Agency (DARPA) for a second MobileSearch(TM) system with enhanced
      operating and detection capabilities. Delivery is anticipated for the
      second quarter of fiscal 1998.

-     The Company's core security market has expanded as more government
      agencies, both U.S. and international, have ordered AS&E's Backscatter
      detection systems for protection against sophisticated terrorist threats.
      Orders totaling $6.2 million were received during fiscal 1997 for


                                       12
<PAGE>   13
      X-ray systems to protect the U.S. offices of two prestigious Federal
      agencies. International revenues increased 45% to $4.8 million in fiscal
      1997 from $3.3 million in fiscal 1996.

-     Throughout the fiscal year the Company improved its position in both the
      domestic and international marketplace, adding fourteen new government
      sector and corporate customers to its base.

The Company's improved sales volume, profitability and liquidity has permitted
increased investments in professional staff, internal technology and
Company-funded research and development in order to support future business
expansion.


ITEM 8.   FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

The financial statements and supplementary financial information listed in the
Index to Consolidated Financial Statements and Schedule on page 28 are filed as
part of this Annual Report on Form 10-K and are incorporated into this Item by
reference.

ITEM 9. CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
        FINANCIAL DISCLOSURE

None.


                                       13
<PAGE>   14
PART III

ITEM 10. DIRECTORS AND EXECUTIVE OFFICERS OF THE COMPANY

-  DIRECTORS AND EXECUTIVE OFFICERS OF THE COMPANY AS OF JUNE 30, 1998.

<TABLE>
<CAPTION>
                                   Positions and Offices of    Date Assumed
Name                     Age       Company Held                Each Position
----                     ---       ------------                -------------
DIRECTORS
<S>                      <C>       <C>                         <C>
Herman Feshbach          81        Director                    September 1975
                                   Chairman                    July 1993

Al Gladen                60        Director                    September 1995

Hamilton W. Helmer       51        Director                    February 1993

Donald J. McCarren       58        Director                    February 1993

William E. Odom          65        Director                    September 1996

Carl W. Vogt             62        Director                    June, 1997

Ralph S. Sheridan        48        Director                    January  1994
                                   President & CEO             September 1993
</TABLE>


EXECUTIVE OFFICERS (Who are not also Directors)


<TABLE>
<S>                      <C>       <C>                         <C>
Jeffrey A. Bernfeld      41        Vice President, General     February 1996
                                   Counsel & Clerk

Joseph Callerame         48        Vice President, Technology  June 1998
                                   Chief Technology Officer

Peter W. Harris          44        Vice President, Sales       March 1994

Alan H. Rutan            57        Vice President, Engineering July 1996

Lee C. Steele            49        Vice President, Finance     September 1994
                                   Treasurer & CFO
</TABLE>

All Directors and Executive Officers hold office until the next annual meeting
of Stockholders and until their successors are duly elected and qualified. No
family relationship exists between any of the listed Directors and Executive
Officers.

Dr. Herman Feshbach is an Institute Professor Emeritus at the Massachusetts
Institute of Technology, a position he has held for more than five years, and
has previously served as Chairman of the Physics Department at MIT and Director
of the MIT Center for Theoretical Physics. He is a past President of the
American Physical Society and the American Academy of Arts and Sciences and is
Fellow of both those Organizations and of the American


                                       14
<PAGE>   15
Association for the Advancement of Sciences. He is on the Board of Governors for
Tel Aviv University and the Weizmann Institute of Science, is on the Board of
Editors for Daedalus and Editor of the Annals of Physics, and has served as
Chairman or Member on numerous committees for the Department of Energy, the
National Science Foundation, the National Academy of Sciences, and the American
Physical Society. He was awarded the National Medal of Science by President
Reagan in 1986. Dr. Feshbach received his Ph.D. from MIT.

Mr. Al Gladen is President of Dabster, Inc., a technology consulting firm
specializing in engineering and technology management assistance, with offices
in Kent, Washington. Mr. Gladen's consulting activities have included strategic
technology planning, new product development, project management and acquisition
review. Mr. Gladen has acted as a technology and engineering consultant to the
Company since 1993, and it is expected that he will continue to provide such
assistance on a part-time basis. Mr. Gladen holds four U.S. patents and is a
director of four other privately held corporations.

Dr. Hamilton W. Helmer has, for the last 15 years, been Managing Partner of
Helmer & Associates, a strategic consulting firm located in Los Altos,
California. Prior to that, Dr. Helmer worked for Bain & Co. Dr. Helmer holds a
Ph.D. in Economics from Yale University.

Dr. Donald J. McCarren is President of the National Center for Genome Resources,
a non-profit corporation located in Santa Fe, New Mexico, which supports genome
projects and related research by providing resources such as expertise in
bioinformatics. Prior to assuming that position in 1997, Dr. McCarren was
President and Chief Executive Officer of Tacora Corporation, a medical
technology company located in Seattle, Washington. From July 1992 to June 1994,
he was President and Chief Operating Officer of ImmunoGen, Inc., a bio-tech
research and development company located in Cambridge, Massachusetts. Prior to
that, he was President (1990 to 1992) of the Adria Laboratories Division of
Erbamont N.V. in Columbus, Ohio, and Corporate Vice President of Worldwide
Marketing and Business Development (1989 to 1990) and Vice President of Far East
and Australian Operations (1986 to 1989) of Erbamont, N.V. Dr. McCarren holds a
Ph.D. in Developmental Economics.

General William E. Odom is the Director of National Security Studies for the
Hudson Institute in Washington, D.C. and an adjunct Professor in the Department
of Political Science at Yale University. Prior to joining the Hudson Institute
in 1988, General Odom spent 34 years as an officer in the United States Army,
retiring with the rank of Lieutenant General. While on active duty, General Odom
served as Director of the National Security Agency for three years, Assistant
Chief of Staff for Intelligence for the Department of the Army for four years
and Military Assistant to the President's National Security Advisor for four
years. General Odom received his B.S. degree from West Point and Masters and
Ph.D. degrees from Columbia University. General Odom is on the Board of
Directors of Nichols Research Corporation of Huntsville, Alabama, V-ONE
Corporation of Rockville, Maryland, Middlebury College, from which he received
an honorary doctorate, and the Institute for the Study of Diplomacy at
Georgetown University. General Odom is the author of five books and numerous
articles.

Mr. Ralph S. Sheridan was elected President and Chief Executive Officer of the
Company in September 1993, and in January of 1994, he was elected a Director.
Prior to joining the Company, Mr. Sheridan ran his own consulting and investment
firm, Value Management Corporation, in Waltham, Massachusetts. Prior to that,
Mr. Sheridan was President and CEO (1988-1989) and Vice President of Marketing
and Operations (1987-1988) of HEC Energy


                                       15
<PAGE>   16
Corp., in Boston, Massachusetts. Before joining HEC, Mr. Sheridan held the
position of Vice President of Operations for the Engineered Systems and Controls
Group (1984-1986) and Vice President of Corporate Business Development
(1981-1984) at Combustion Engineering, Inc. in Stamford, Connecticut. Mr.
Sheridan holds a B.S. in Chemistry and an M.B.A., both from Ohio State
University.

Mr. Carl W. Vogt was elected to the Board in June, 1997. He is a partner in the
Washington, D.C. office of the national law firm of Fulbright & Jaworski. Mr.
Vogt has been with that firm since 1966, with various periods away from the firm
to perform government service. In 1992, he was appointed by President Bush as
the Chairman of the National Transportation Safety Board, where he served until
1994. Mr. Vogt earned his bachelor's degree from Williams College and his law
degree from the University of Texas Law School.

Mr. Jeffrey A. Bernfeld joined AS&E as Vice President, General Counsel and Clerk
in February 1996. Prior to that time, he was Vice President and General Counsel
of Spire Corporation in Bedford, Massachusetts for three and one-half years; a
founder and Managing Director of Global Solutions, Inc. in Wellesley,
Massachusetts for one year; Vice President and General Counsel of The Mediplex
Group in Wellesley, Massachusetts for two years; and a partner at Goldstein &
Manello, a law firm in Boston, Massachusetts, where he began his career as an
Associate in 1981. Mr. Bernfeld received his B.A. from Brandeis University and
his J.D. from New York University School of Law. Mr. Bernfeld is a director of
Summit Technology, Inc. of Waltham, Massachusetts.

Dr. Joseph Callerame joined American Science & Engineering in June 1998 as Vice
President, Technology, and Chief Technology Officer. Prior to joining AS&E, Dr.
Callerame spent over twenty years at Raytheon Company, most recently as Manager,
Engineering and Technology Development and Consulting Scientist, at Raytheon
Electronic Systems. Prior to that appointment, Dr. Callerame was Deputy General
Manager of Raytheon's Corporate Research Division. Dr. Callerame received his
B.A. in Physics from Columbia College, and his M.A. and Ph.D., also in Physics,
from Harvard University. After receiving his Ph.D. and prior to his employment
at Raytheon, Dr. Callerame served as a Post-Doctoral Fellow in Nuclear Physics
at M.I.T.

Mr. Peter W. Harris joined the Company in February 1994 as Vice President, Sales
and Marketing. Prior to joining the Company, Mr. Harris was Manager of External
Affairs for Stone & Webster, an architectural engineering firm in Boston,
Massachusetts, where he held a number of positions beginning in 1988. During his
time at Stone & Webster, Mr. Harris concentrated on Federal government and
international sales. Mr. Harris, a graduate of the U.S. Naval Academy, holds the
rank of Captain in the U.S. Naval Reserve and commanded several units during his
twelve years of active duty and seven years in the Naval Reserve. In addition,
Mr. Harris holds a Master's degree in National Security Studies from Georgetown
University.

Mr. Alan H. Rutan joined the Company in July 1996 as Vice President of
Engineering. Prior to that time, Mr. Rutan spent 11 years at Raytheon Company,
most recently as Manager of the Air Defense Systems Department, where his work
focused on radar systems engineering and signal processing. Prior to his
Raytheon experience, Mr. Rutan spent seven years at GTE Laboratories as a Senior
Member of the Technical Staff. From 1974 to 1978, Mr. Rutan ran his own
consulting firm, Signal Processing Associates, Inc., which specialized in image
processing


                                       16
<PAGE>   17
applications for various government security organizations. Mr. Rutan
received his B.A. in Physics from Harvard University.

Mr. Lee C. Steele joined the Company in September 1994 as Vice President of
Finance and Chief Financial Officer. From 1991 until he joined the Company, Mr.
Steele was a principal of Asset Management Corporation, a Waltham, Massachusetts
consulting firm specializing in the analysis and resolution of complex financial
and operational challenges for small and medium size businesses. Until 1991, Mr.
Steele was a Partner at Deloitte & Touche, specializing in profit planning,
corporate finance and troubled company situations. He holds an M.B.A. from
Harvard Business School and an engineering degree from Case Western Reserve
University.


ITEM 11.   EXECUTIVE COMPENSATION

-  THE FOLLOWING CHART PROVIDES INFORMATION CONCERNING COMPENSATION PAID BY THE
   COMPANY DURING THE YEAR ENDED MARCH 31, 1998 TO THE CHIEF EXECUTIVE OFFICER
   AND EACH OF THE FOUR MOST HIGHLY COMPENSATED EXECUTIVE OFFICERS OF THE
   COMPANY WHOSE AGGREGATE COMPENSATION EXCEEDED $100,000.

                              SUMMARY COMPENSATION

<TABLE>
<CAPTION>
                                                            Annual                    Long-Term
                                                         Compensation                  Compen-
                                                 -------------------------------       sation                    All
Name and Principal              Fiscal                                                  Option               OtherCompen-
Position                        Year             Salary ($)            Bonus ($)       Awards (#)           sation ($) (1)
----------------------------    ------           -----------           ---------       ----------           --------------
<S>                             <C>              <C>                   <C>             <C>                  <C>
Ralph S. Sheridan               1998                 240,000             230,000                0                 7,729
President and CEO               1997                 222,213             270,385(3)       225,000                 4,479
                                1996                 200,000             202,168(3)             0                 2,486

Jeffrey A. Bernfeld             1998                 130,000              30,000           20,000                   408
Vice President, General         1997                 120,408              19,000           16,000                   408
Counsel                         1996(2)                7,846                N.A.           24,000                   408

Peter W. Harris                 1998                 120,192              45,000                0                   403
Vice President,                 1997                 111,941              45,000           30,000                   403
Sales / Marketing               1996                 110,000              40,000                0                   403

Alan H. Rutan                   1998                 115,112              12,000           16,000                 1,748
Vice President                  1997(2)               87,132                  --           24,000                 1,748
Engineering

Lee C. Steele                   1998                 125,077              29,750           30,000                   752
Vice President and              1997                 120,560              27,000                0                   752
CFO                             1996                 110,752              27,000                0                 1,344
</TABLE>



                                       17
<PAGE>   18
(1)   All Other Compensation includes imputed income from taxable life insurance
      premiums paid by the Company, and, for Mr. Sheridan, a leased automobile.

(2)   The indicated years were years of partial employment with the Company for
      the named executive.

(3)   Mr. Sheridan's bonus is paid in respect of "contract years" ending
      September 30th in each year and is paid in cash, except in fiscal years
      1996 and 1997 when the bonus also included Company stock and payments made
      to him to alleviate the tax impact of the stock bonus.

Mr. Sheridan has an employment contract with the Company that provides for his
employment as President and Chief Executive Officer, and as a Director, through
September 1999, at an annual salary of $240,000, subject to annual review, plus
performance bonuses tied to specific accomplishments. This contract replaces Mr.
Sheridan's original contract with the Company, which expired in September 1996.

Under the contract, Mr. Sheridan is eligible to receive an annual bonus of up to
$230,000 in each contract year, based on his accomplishment of goals established
by the Compensation Committee. Under the previous contract, but not under the
current contract, Mr. Sheridan also received a bonus of up to 10,000 shares of
common stock and an amount calculated to compensate him for the taxes due on the
stock portion of this bonus. In addition, in October 1996 the Company granted
Mr. Sheridan options to purchase 225,000 shares of the Company's Common Stock at
an exercise price of $14.00 per share, the fair market value of the Company's
Common Stock on the date of grant. The options become exercisable at the rate of
75,000 options per year on the first three anniversaries of the grant.

Mr. Sheridan recognized no income upon the issuance of the options. When the
options are exercised, Mr. Sheridan will recognize ordinary income in an amount
equal to the difference between the fair market value of the Common Stock
received upon the exercise of the option and the amount paid for the Common
Stock. At that time, the Company will be allowed a deduction equal to the amount
recognized as ordinary income by Mr. Sheridan. The options provide that to the
extent that exercise of an option would give rise to compensation expense that
the Company reasonably expects will not be deductible for tax purposes in any
given taxable year pursuant to Section 162(m) of the Internal Revenue Code of
1986, as amended, the number of shares as to which the options may be exercised
during that taxable year shall be limited.

Under his initial employment contract, Mr. Sheridan purchased 160,000 treasury
shares of the Company's Common Stock payable by promissory note. The note is due
on the earlier of September 15, 2003 or the termination of Mr. Sheridan's
employment. The Company has agreed to reimburse Mr. Sheridan for the interest
payable under the note in most circumstances.

Mr. Sheridan is entitled to receive the same benefits as other senior executives
of the company, as well as to the use of a car.

In the event that Mr. Sheridan's employment with the Company is terminated
without Cause, or by him for Good Reason (as defined in the employment
contract), he will receive twelve months' pay and any previously earned bonuses.
In the event that Mr. Sheridan's employment with the Company is terminated for
Cause, or by him other than for Good Reason (as defined in the employment
contract), or by his death or disability, he will not be entitled to receive any
salary beyond the date of termination, and he will only be entitled to receive
previously earned bonuses if the termination is caused by death or disability.

Mr. Bernfeld has an agreement with the Company which provides for a minimum base
salary of $120,000, adjustable at the discretion of the President, and a bonus
of up to $20,000 subject to the


                                       18
<PAGE>   19
achievement of individual and corporate goals; and 24,000 stock options granted
at market price, which vest according to a schedule. The agreement is for a
three year term ending in February, 1999, and grants Mr. Bernfeld severance
payments equal to one year's salary if he is terminated in connection with a
change of the control of the Company as defined in the agreement. The agreement
also provides that if Mr. Bernfeld is terminated for any reason other than
"Cause" as defined in the agreement, he will be entitled to receive an amount
equal to at least six months salary.

Dr. Callerame and Messrs. Rutan and Steele have agreements with the Company
granting each of them severance payments equal to one year's salary if he is
terminated in connection with a change of control of the Company as defined in
the agreement. The agreement also provides that if each of them is terminated
for any reason other than "Cause" as defined in the agreement, he will be
entitled to receive an amount equal to at least six months salary.


-  THE FOLLOWING TABLES PROVIDE INFORMATION CONCERNING THE GRANT OF OPTIONS IN
   FISCAL YEAR 1998 TO EXECUTIVE OFFICERS NAMED IN THE SUMMARY COMPENSATION
   TABLE AND OPTIONS EXERCISED BY THOSE OFFICERS.


                      OPTION GRANTS IN THE LAST FISCAL YEAR

<TABLE>
<CAPTION>
                                                    Individual Grants                        Potential Realizable Value
                             --------------------------------------------------------------  at Assumed Annual Rates
                                                                                             of Stock Price
                                                                                             Appreciation for Option
                                                                                             Term ($)
                                                                                             ----------------------------------
                                                    % of Total
                                                       Options
                                                    Granted to
                                     Options               All     Exercise     Expiration
                                     Granted         Employees     Price ($)           Date          5%/year           10%/year
                                     -------        ----------     ---------   -------------         --------          --------
<S>                                  <C>            <C>            <C>          <C>                   <C>               <C>
Ralph S. Sheridan                          0               N/A           N/A            N/A               N/A               N/A
Jeffrey A. Bernfeld                   20,000              6.98        11.125       11/20/07           221,374           484,295
Peter W. Harris                            0               N/A           N/A            N/A               N/A               N/A
Alan H. Rutan                         16,000              5.58        11.125       11/20/07           177,099           387,436
Lee C. Steele                         30,000             10.47        11.125       11/20/07           332,061           726,442
</TABLE>


                                       19
<PAGE>   20
                 AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR
                        AND FISCAL YEAR END OPTION VALUES


<TABLE>
<CAPTION>
                                                                            Number of                Value of Unexercised In-
                                                                      Unexercised Options              The-Money Options at
                                      Shares                         at Fiscal Year End -               Fiscal Year End -
                                    Acquired                           March 31, 1998 (#)               March 31, 1998  ($)
                                          on         Value         -----------------------          -----------------------------
                                    Exercise      Realized         Exerc-        Unexerc-           Exerc-           Unexerc-
                                         (#)           ($)         isable         isable            isable            isable
---------------------------------------------------------------------------------------------------------------------------------
<S>                                <C>            <C>              <C>           <C>                <C>              <C>
Ralph S. Sheridan                          0             0         195,000         150,000          2,176,875                0
Jeffrey A. Bernfeld                        0             0          30,000          30,000            107,250           85,750
Peter W. Harris                            0             0          40,000          20,000            318,250           75,000
Alan H. Rutan                              0             0          12,000          28,000             43,500           83,500
Lee C. Steele                              0             0          50,000          30,000            409,375           75,000
</TABLE>


-  COMPENSATION OF DIRECTORS

Directors who are also employees of the Company do not receive additional
compensation as Directors. Non-Employee Directors (other than the Chairman)
receive annual compensation of 2,000 shares of Company Common Stock issuable on
January 10th in each year, and options to purchase 7,000 shares of Common Stock
at the closing price on the date of the Annual Meeting in each year. The
Chairman receives 2,500 shares of Common Stock on January 10th in each year and
continues to receive deferred compensation under a now discontinued plan
described below. No meeting fees or other fees are payable to any Director. See
Item 13 - Certain Relationships and Related Transactions for additional
information concerning certain Directors.

Dr. Feshbach, the Company's Chairman, is covered by a nonfunded deferred
compensation plan (adopted in 1976 and amended in 1977, 1980, 1986, 1990 and
1992) that provides for periodic payments beginning at age 65, based on length
of service. During the year, Dr. Feshbach received $4,752 under the Plan. The
Company accrues the current cost of the plan, which amounted to $10,000 in
fiscal 1998.

-  COMPENSATION COMMITTEE INTERLOCKS, INSIDER PARTICIPATION AND SECTION 16
   REPORTING

During the fiscal year ended March 31, 1998, the Company's Compensation
Committee consisted of Dr. Herman Feshbach, Dr. Hamilton W. Helmer and Dr.
Donald J. McCarren. No reportable relationship existed with respect to any
member of the Compensation Committee.

Section 16(a) of the Securities Exchange Act of 1934 requires certain persons,
including the Company's Directors and Executive Officers, to file initial
reports of beneficial ownership of the Company's securities and reports of
changes in beneficial ownership with the Securities and Exchange Commission. For
fiscal year 1998, the Company believes that all required reports were filed on
time.

-  BOARD COMPENSATION COMMITTEE REPORT ON EXECUTIVE COMPENSATION

The Compensation Committee of the Board of Directors (consisting of the three
outside Directors whose names appear below this Report) has sole responsibility
for compensation issues relating to the Chief


                                       20
<PAGE>   21
Executive Officer. Compensation practices and policies for the other executive
officers are set by the Chief Executive Officer with the advice of the
Compensation Committee.

The Compensation Committee has formulated an approach to all executive
compensation that emphasizes the establishment of goals and objectives for each
executive and for the Company as a whole and ties a substantial portion of
executive compensation to the performance of the executive and the Company with
respect to these goals and objectives. Base compensation for executive officers
(and many other Company employees) is established on the basis of an analysis of
salaries received by comparable employees of high-tech and manufacturing
companies in the Greater Boston area, company financial results and prospects,
and individual contributions relative to the job description and past
performance of each officer.

In line with this approach, the Company entered into a new employment agreement
with its President and Chief Executive Officer, Mr. Ralph S. Sheridan, in 1996
(effective as of September 1996). This Agreement was based, in part, on an
independent consultant's analysis of compensation arrangements for chief
executives of comparable companies, and was also based on a careful review of
the most important goals and objectives for the Company. The Agreement provides
for annual cash compensation of $240,000, plus annual incentive bonuses of up to
$230,000 tied to specific, agreed upon performance criteria. In addition, in
order to provide for long-term incentives, the Company has issued to Mr.
Sheridan nonstatutory stock options to purchase 225,000 shares of Common Stock
which vest ratably over three years.

For the contract year ended in September 1997, the Committee awarded Mr.
Sheridan a cash bonus of $230,000, representing 100% of the potential award
under his contract. This award represents the Committee's determination that Mr.
Sheridan had done an excellent job over the preceding twelve months and had met
all of the goals and objectives jointly established by the Committee and Mr.
Sheridan.

Also in keeping with its performance-based compensation philosophy, in the
spring of 1994, the Company implemented an incentive compensation program for
all executives who report directly to the Office of the President. Under this
new policy, these executives receive a specified portion of their total
compensation (ranging from 10% to 50%) based upon two factors: their completion
of agreed upon goals and objectives, and the performance of the entire Company.

Report Submitted By: Dr. Herman Feshbach, Dr. Hamilton W. Helmer and Dr. Donald
J. McCarren.


                                       21
<PAGE>   22

-  STOCK PERFORMANCE CHART

The following chart graphs the performance of the cumulative total return to
shareholders (stock price appreciation plus dividends) during the previous five
years in comparison to the returns of the Standard & Poor's 500 Composite Stock
Price Index and the Standard & Poor's 500 High-Tech Composite Stock Price Index.


                          [TOTAL SHAREHOLDER RETURNS]


                                INDEXED RETURNS
                                  Years Ending

<TABLE>
<CAPTION>
                                 BASE
                                PERIOD
COMPANY/INDEX                   MAR 93       MAR 94       MAR 95     MAR 96     MAR 97    MAR 98
------------------------------------------------------------------------------------------------
<S>                              <C>        <C>          <C>        <C>        <C>       <C>
AMERICAN SCIENCE ENGINEERING      100         46.97        75.76     119.70     146.97    165.15
S&P 500 INDEX                     100        101.48       117.25     154.77     185.40    274.39
TECHNOLOGY-500                    100        117.62       148.84     200.95     271.66    410.57
</TABLE>

Note: Assumes $100 invested at the close of trading on the last trading day
      preceding the first day of the fifth preceding fiscal year (and
      reinvestment of dividends) in the Company's Common Stock, Standard &
      Poor's 500 Composite Stock Price Index and the Standard & Poor's 500
      High-Tech Composite Stock Price Index.


                                       22
<PAGE>   23
ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

-     THE FOLLOWING CHART SHOWS THE COMPANY COMMON STOCK BENEFICIALLY OWNED BY
      OFFICERS AND DIRECTORS OF THE COMPANY ON JUNE 30, 1998. BASED ON
      INFORMATION AVAILABLE TO IT, THE COMPANY BELIEVES THAT NO OTHER PERSON OR
      ENTITY OWNED 5 PERCENT OR MORE OF THE COMPANY'S COMMON STOCK ON THAT DATE.

<TABLE>
<CAPTION>
Name of                           Amount and Nature of       Percent
Beneficial Owner                 Beneficial Ownership(1)     of Class
----------------                 -----------------------     --------
<S>                              <C>                         <C>
Jeffrey A. Bernfeld                       32,591               (2)
Joseph Callerame                          15,000               (2)
Herman Feshbach                           16,540               (2)
Al Gladen                                 53,055               1.12
Peter W. Harris                           43,177               (2)
Hamilton W. Helmer                        46,781               (2)
Donald J. McCarren                        54,581               1.14
William E. Odom                           12,000               (2)
Alan H. Rutan                             35,140               (2)
Ralph S. Sheridan                        401,743               8.13
Lee C. Steele                             59,096
Carl W. Vogt                              14,166
Directors and Officers
    as a Group (12 persons)              783,870               15.1
</TABLE>

(1)   Includes shares that may be acquired under stock options and warrants
      exercisable within sixty days after the date of this table, as follows:
      Mr. Bernfeld - 30,000; Dr. Callerame - 12,500; Dr. Feshbach - 2,500; Mr.
      Gladen - 14,000; Mr. Harris - 40,000; Dr. Helmer - 39,000; Dr. McCarren -
      40,000; Mr. Odom - 7,000; Mr. Rutan -18,000; Mr. Sheridan - 195,000; Mr.
      Steele - 50,000; Mr. Vogt - 0; and all Directors and Officers as a group -
      448,000. All ownership reported herein includes sole voting and investment
      power.

(2)   Amount owned constitutes less than one percent.


ITEM 13.   CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

In April, 1995 a group that included three of the Company's Officers and one
Company Director made a loan to the Company in the total amount of $650,000. The
proceeds of the loan were used for general working capital purposes. The loan
was paid off in full on a timely basis.

The Board of Directors determined that the loan was necessary and the terms
appropriate. The Company had been seeking short-term financing from several
banks, but conclusion of a conventional line of credit arrangement was delayed
pending resolution of the lawsuit brought by the Company's founder, in which the
Company has now received a favorable jury verdict. In addition, portions of the
Company's working capital had been tied up in slow-paying foreign accounts
receivable and as collateral for letters of credit supporting certain
international sales. These factors justified a form of short-term "bridge loan"
while the Company worked on a more permanent financing alternative.

The loan terminated on August 15, 1995, and bore interest at the prime rate plus
two percent. The Company granted a security interest in all of its assets to the
lending group during the pendency of the


                                       23
<PAGE>   24
loan. As additional consideration, the Company issued a total of 6,500 shares of
its Common Stock and warrants to purchase 65,000 shares of its Common Stock
proportionally to the lenders. The warrant exercise price is the lowest trading
price of the stock on the American Stock Exchange during the term of the loan.
The Company has registered these shares.

Ralph S. Sheridan, the Company's President and CEO, provided $200,000 of the
loan funds. Al Gladen, who subsequently became a Director of, and remains a
Consultant to, the Company, provided $300,000. Lee C. Steele, the Company's Vice
President of Finance and CFO, provided $75,000. Donald J. McCarren, a Director
of the Company, provided $50,000. Peter W. Harris, the Company's Vice President
of Sales and Marketing, provided $25,000.

Mr. Gladen provides engineering and management services to the Company on a
regular basis. In fiscal year 1998, the compensation paid to Dabster, Inc., a
corporation of which Mr. Gladen is the President, for such services was
$256,750.

All other information required for by this Item appears in Items 10 and 11 of
this Annual Report on Form 10-K, and is incorporated herein by reference.



PART IV

ITEM 14. EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K

(a)   The financial statements and schedules listed in the Index to Consolidated
      Financial Statements and Schedule on page 28 are filed as part of this
      report, and such Index is incorporated in this Item by reference.

      The exhibits listed in the Exhibit Index on page 47-48 are filed as part
      of this report, and such Index is incorporated in this Item by reference.

(b)   Reports on Form 8-K. There were no reports on Form 8-K filed during the
      fourth quarter of the fiscal year covered by this report.


                                       24
<PAGE>   25
             AMERICAN SCIENCE AND ENGINEERING, INC., AND SUBSIDIARY
             INDEX TO CONSOLIDATED FINANCIAL STATEMENTS AND SCHEDULE

(Submitted in answer to Item 8 and Item 14 of Form 10-K, Securities and Exchange
Commission)

<TABLE>
<CAPTION>
CONSOLIDATED FINANCIAL STATEMENTS                                                  PAGE
<S>                                                                                <C>
Report of Independent Public Accountants                                            26
Consolidated Balance Sheets - March 31, 1998 and March 28, 1997                     27-28
Consolidated Statements of Operations                                               29
      For the Years Ended March 31, 1998 March 28, 1997, and March 29, 1996
Consolidated Statements of Stockholders' Investment                                 30
      For the Years Ended March 31, 1998 March 28, 1997,
      and March 29, 1996
Consolidated Statements of Cash Flows                                               31
      For the Years Ended March 31, 1998 March 28, 1997,
      and March 29, 1996
Notes to Consolidated Financial Statements - March 31, 1998                         32-43

CONSOLIDATED SUPPLEMENTARY FINANCIAL INFORMATION

Unaudited quarterly consolidated financial data for
      the years ended March 31, 1998, and March 28, 1997                            44


(Separate Financial Statements of the Company have been omitted since the net
assets of its wholly owned subsidiary are not so restricted with respect to
payment of loans, advances and cash dividends to the Company as to require such
disclosure.)

FINANCIAL STATEMENT SCHEDULE

Schedule II - Valuation and Qualifying Accounts and Reserves                         45
</TABLE>


Other schedules have been omitted because of the absence of conditions under
which they are required or because the required information is given in the
financial statements or notes thereto.


                                       25
<PAGE>   26
                    REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS


To American Science and Engineering, Inc.:

We have audited the accompanying consolidated balance sheets of American Science
and Engineering, Inc. (a Massachusetts corporation) and subsidiary as of March
31, 1998 and March 28, 1997 and the related consolidated statements of
operations, stockholders' investment and cash flows for each of the three years
in the period ended March 31, 1998. These consolidated financial statements and
the schedule referred to below are the responsibility of the Company's
management. Our responsibility is to express an opinion on these consolidated
financial statements and schedule based on our audits.

We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

In our opinion, the consolidated financial statements referred to above present
fairly, in all material respects, the consolidated financial position of
American Science and Engineering, Inc. and subsidiary as of March 31, 1998 and
March 28, 1997, and the results of their operations and their cash flows for
each of the three years in the period ended March 31, 1998 in conformity with
generally accepted accounting principles.

Our audits were made for the purpose of forming an opinion on the basic
consolidated financial statements taken as a whole. The schedule listed in the
index to consolidated financial statements and schedule is presented for
purposes of complying with the Securities and Exchange Commission's rules and is
not part of the basic consolidated financial statements. This schedule has been
subjected to the auditing procedures applied in the audit of the basic
consolidated financial statements and, in our opinion, fairly states in all
material respects the financial data required to be set forth therein in
relation to the basic consolidated financial statements taken as a whole.


/s/ ARTHUR ANDERSEN LLP


Boston, Massachusetts
May 14, 1998


                                       26
<PAGE>   27
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                           CONSOLIDATED BALANCE SHEETS
                        MARCH 31, 1998 AND MARCH 28, 1997
                              Dollars in thousands

<TABLE>
<CAPTION>
ASSETS                                                     1998          1997
                                                         -------       -------
CURRENT ASSETS:
<S>                                                     <C>           <C>
Cash and cash equivalents (Note 2)                       $ 2,290       $ 3,202
Accounts receivable, net of allowances of
  $116 in 1998 and $148 in 1997 (Note 1)                   6,955         4,885
Unbilled costs and fees, net of allowances of
  $549 in 1998 and $462 in 1997 (Note 1)                   3,190           981
Inventories (Note 1)                                       8,737         4,736
Deferred income taxes (Notes 1 and 5)                      2,351            --
Prepaid expenses and other current assets                    389           291
                                                         -------       -------
TOTAL CURRENT ASSETS                                      23,912        14,095
                                                         -------       -------
Non-current deferred income taxes (Note 1 and 5)             205            --
Deposits                                                      24           115
Property, equipment and leasehold
  improvements, net of accumulated depreciation
  of $9,394 in 1998 and $8,860 in 1997
  (Notes 1 and 3)                                          1,852         1,304
                                                         -------       -------
                                                         $25,993       $15,514
                                                         =======       =======
</TABLE>

The accompanying notes are an integral part of these consolidated financial
statements.


                                       27
<PAGE>   28
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                     CONSOLIDATED BALANCE SHEETS (CONTINUED)
                        MARCH 31, 1998 AND MARCH 28, 1997
                              Dollars in thousands

<TABLE>
<CAPTION>
Liabilities & Stockholders' Investment                         1998            1997
                                                             --------        --------
<S>                                                          <C>             <C>
Current liabilities:
Current maturities of obligations
  under capital leases (Note 3)                              $     20        $     18
Accounts payable                                                4,360           2,253
Accrued salaries and benefits                                     831             573
Accrued warranty costs (Note 1)                                   497             292
Accrued income taxes (Notes 1 and 5)                              615              90
Deferred revenue (Note 1)                                       1,240             526
Customer deposit (Note 1)                                       1,151              --
Other current liabilities                                         507             487
                                                             --------        --------
TOTAL CURRENT LIABILITIES                                       9,221           4,239
                                                             --------        --------

NON-CURRENT LIABILITIES:
Obligations under capital leases, net
   of current maturities (Note 3)                                  22              42
Deferred revenue (Note 1)                                         232             660
Deferred compensation (Note 11)                                   154             174
Deferred rent (Note 1)                                            280             249
                                                             --------        --------
TOTAL NON-CURRENT LIABILITIES                                     688           1,125
                                                             --------        --------


COMMITMENTS AND CONTINGENCIES (Notes 3, 4, and 11)

STOCKHOLDERS' INVESTMENT: (Notes 6 and 7)
Preferred stock, no par value
  Authorized - 100,000 shares
  Issued - None
Common stock, $.66-2/3 par value
  Authorized - 20,000,000 shares Issued
  4,743,569 shares in 1998
  and 4,585,209 shares in 1997                                  3,162           3,058
Capital in excess of par value                                 16,278          15,273
Accumulated deficit                                            (2,704)         (7,365)
                                                             --------        --------
                                                               16,736          10,966
Note receivable-Officer (Note 8)                                 (640)           (640)
Less: treasury stock - 6,678 and
  62,841 shares in 1998 and
  in 1997, at cost, respectively                                  (12)           (176)
                                                             --------        --------
TOTAL STOCKHOLDERS' INVESTMENT                                 16,084          10,150
                                                             --------        --------
                                                             $ 25,993        $ 15,514
                                                             ========        ========
</TABLE>

The accompanying notes are an integral part of these consolidated financial
statements.


                                       28
<PAGE>   29
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                      CONSOLIDATED STATEMENTS OF OPERATIONS
     FOR THE YEARS ENDED MARCH 31, 1998, MARCH 28, 1997, AND MARCH 29, 1996
                 Dollars in thousands, except per share amounts

<TABLE>
<CAPTION>
                                                          1998            1997              1996
                                                          ----            ----              ----
<S>                                                <C>             <C>              <C>
NET SALES AND CONTRACT REVENUES
  (Notes 1 and 10)                                 $    32,699     $    28,479      $     17,815
Cost of sales and contracts (Note 1)                    19,816          18,423            11,823
                                                   -----------     -----------      ------------
GROSS PROFIT                                            12,883          10,056             5,992

EXPENSES:
Selling, general and administrative                      7,425           6,494             4,588
Research and development (Note 1)                        2,856           1,602               533
                                                   -----------     -----------      ------------
TOTAL EXPENSES                                          10,281           8,096             5,121
                                                   -----------     -----------      ------------

OPERATING INCOME                                         2,602           1,960               871
                                                   -----------     -----------      ------------

OTHER INCOME/(EXPENSE):
Interest, net                                              118             111                52
Other, net                                                 (22)            (68)              (91)
                                                   -----------     -----------      ------------
TOTAL OTHER INCOME (EXPENSE)                                96              43               (39)
                                                   -----------     -----------      ------------

INCOME BEFORE PROVISION FOR (BENEFIT FROM)
   INCOME TAXES                                          2,698           2,003               832
PROVISION FOR (BENEFIT FROM) INCOME TAXES
   (NOTE 5)                                            (1,963)              78                30
                                                   -----------     -----------      ------------

NET INCOME                                         $   4,661       $     1,925      $        802
                                                   ===========     ===========      ============

INCOME PER SHARE               - BASIC               $    1.00      $      .43        $      .18
                                                   ===========     ===========      ============
                               - DILUTED            $      .95      $      .40        $      .18
                                                   ===========     ===========      ============

WEIGHTED AVERAGE SHARES        - BASIC                   4,646           4,491             4,387
                                                   ===========     ===========      ============
                               - DILUTED                 4,917           4,826             4,541
                                                   ===========     ===========      ============
</TABLE>

The accompanying notes are an integral part of these consolidated financial
statements.


                                       29
<PAGE>   30
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
               CONSOLIDATED STATEMENTS OF STOCKHOLDERS' INVESTMENT
     FOR THE YEARS ENDED MARCH 31, 1998, MARCH 28, 1997, AND MARCH 29, 1996
                   Amounts in thousands, except share amounts

<TABLE>
<CAPTION>
                                                    CAPITAL IN       ACCU-         NOTE
                               COMMON STOCK          EXCESS OF       MULATED     RECEIVABLE       TREASURY STOCK
                          SHARES         AMOUNT      PAR VALUE       DEFICIT       OFFICER       SHARES        AMOUNT         TOTAL
                         ---------       ------       -------       --------        -----        -------        -----        -------
<S>                      <C>             <C>          <C>           <C>             <C>           <C>           <C>          <C>
BALANCE,
MARCH 31, 1995           4,257,120       $2,838       $13,612       $(10,092)       $(640)        67,377        $(126)       $ 5,592

Net income                      --           --            --            802           --             --           --            802
Exercise of stock
  options (Note 6)          18,868           13            40             --           --             --           --             53
Issuance of stock
  (Note 7)                 224,639          150           904             --           --             --           --          1,054
                         ---------       ------       -------       --------        -----        -------        -----        -------

BALANCE,
MARCH 29, 1996           4,500,627        3,001        14,556         (9,290)        (640)        67,377         (126)         7,501

Net income                      --           --            --          1,925           --             --           --          1,925
Exercise of stock
  options (Note 6)          68,723           46           396             --           --          5,464          (69)           373
Issuance of stock           15,859           11           321             --           --        (10,000)          19            351
                         ---------       ------       -------       --------        -----        -------        -----        -------

BALANCE,
MARCH 28, 1997           4,585,209        3,058        15,273         (7,365)        (640)        62,841         (176)        10,150

Net income                      --           --            --          4,661           --             --           --          4,661
Exercise of stock
  options (Note 6)         152,735          101           783             --           --             --           --            884
Issuance of stock            5,625            3           222             --           --        (56,163)         164            389
                         ---------       ------       -------       --------        -----        -------        -----        -------

BALANCE,
MARCH 31, 1998           4,743,569       $3,162       $16,278       $ (2,704)       $(640)         6,678        $ (12)       $16,084
                         =========       ======       =======       ========        =====        =======        =====        =======
</TABLE>


The accompanying notes are an integral part of these consolidated financial
statements.


                                       30
<PAGE>   31
               AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                       CONSOLIDATED STATEMENTS OF CASH FLOWS
     FOR THE YEARS ENDED MARCH 31, 1998, MARCH 28, 1997, AND MARCH 29, 1996
                              Dollars in thousands

<TABLE>
<CAPTION>
                                                                  1998           1997           1996
                                                                -------        -------        -------
<S>                                                             <C>            <C>            <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
Net income                                                      $ 4,661        $ 1,925        $   802
Adjustments to reconcile net income to net cash
     provided by (used for) operating activities:
     Depreciation and amortization                                  534            352            205
     Provisions for contract, inventory, accounts
             receivable and warranty reserves                       896            795            510
     Deferred income tax benefit                                 (2,556)            --             --
     Change in assets and liabilities:
             Accounts receivable                                 (2,070)        (1,322)        (1,244)
             Unbilled costs and fees                             (2,409)            (7)           725
             Inventories                                         (4,151)          (422)          (442)
             Prepaid expenses, other assets,
                and deposits                                         (7)           273           (257)
             Accounts payable                                     2,107            232           (148)
             Accrued income taxes                                   525             90             --
             Customer deposits                                    1,151         (2,670)         2,622
             Deferred revenue                                       714            151            181
             Accrued expenses and other
                 current liabilities                                326            111         (1,209)
             Noncurrent liabilities                                (417)           650            221
                                                                -------        -------        -------

     Total adjustments                                           (5,357)        (1,767)         1,164
                                                                -------        -------        -------

     NET CASH PROVIDED BY (USED FOR) OPERATING ACTIVITIES          (696)           158          1,966
                                                                -------        -------        -------

CASH FLOWS FROM INVESTING ACTIVITIES:
     Purchase of property and equipment, net                     (1,082)          (730)          (250)
                                                                -------        -------        -------

CASH FLOWS FROM FINANCING ACTIVITIES:
     Proceeds from exercise of stock options                        884            412             53
     Principal payments of capital lease obligations                (18)           (15)          (158)
     Proceeds from borrowings (Note 11)                              --             --            650
     Repayment of officer note (Note 11)                             --             --           (650)
     Proceeds from issuance of stock                                 --             --            897
                                                                -------        -------        -------
     Cash provided by financing activities                          866            397            792
                                                                -------        -------        -------

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS               (912)          (175)         2,508
CASH AND CASH EQUIVALENTS AT BEGINNING OF YEAR                    3,202          3,377            869
                                                                -------        -------        -------
CASH AND CASH EQUIVALENTS AT END OF YEAR                        $ 2,290        $ 3,202        $ 3,377
                                                                =======        =======        =======

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
     Interest paid                                              $     6        $    10        $    79
     Income taxes paid                                               40             30             --

NON-CASH TRANSACTIONS:
     Issuance of stock in lieu of fees                          $   225        $   332        $   157
     Issuance of treasury stock in lieu of fees                     164             --             --
     Stock option exercises                                          --             30             --
     Common stock received to treasury for stock option
         exercises                                                   --            (69)            --
     Stock bonus issued to Officer from treasury                     --             19             --
</TABLE>

The accompanying notes are an integral part of these consolidated financial
statements.


                                       31
<PAGE>   32
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1998


1.  NATURE OF OPERATIONS AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

American Science and Engineering, Inc., is engaged in the development and
manufacture of sophisticated X-ray inspection systems for critical detection and
security screening solutions for sale primarily to U.S. and foreign government
agencies.

USE OF ESTIMATES The preparation of financial statements in conformity with
generally accepted accounting principles requires management to make estimates
and assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results could differ from those estimates.

PRINCIPLES OF CONSOLIDATION The consolidated financial statements include the
accounts of the Company and its wholly owned subsidiary. All significant
intercompany balances and transactions have been eliminated in consolidation.
Effective the quarter ended September 30, 1997, the Company has elected to
change financial reporting from a fiscal month end to a calendar month end. The
year end reporting period ended on March 31, 1998. This change in year end has
no material effect on the results of operations for the year ended March 31,
1998. The Company's fiscal years ended on March 31, 1998, March 28, 1997, and
March 29, 1996.

INVENTORIES Inventories are stated at the lower of cost, computed on a first-in,
first-out basis, or market and generally include material, labor and factory
overhead.

The components of inventories at March 31, 1998 and March 28, 1997 were as
follows (dollars in thousands):

<TABLE>
<CAPTION>
                                    1998         1997
                                  ------       ------
<S>                               <C>          <C>
Raw materials and completed
   subassemblies                  $4,958       $3,106
Work-in-process                    3,654        1,334
Finished goods                       125          296
                                  ------       ------
                                  $8,737       $4,736
                                  ======       ======
</TABLE>

PROPERTY, EQUIPMENT AND LEASEHOLD IMPROVEMENTS The Company provides for
depreciation and amortization of its fixed assets, principally equipment, using
straight-line and accelerated methods over estimated useful lives of 3-10 years.
Expenditures for normal maintenance and repairs are charged to expense as
incurred. Significant additions, renewals or betterments that extend the useful
lives of the assets are capitalized. The cost and accumulated depreciation
applicable to equipment and leasehold improvements sold or otherwise disposed of
are removed from the accounts, and any resulting gain or loss is included in the
consolidated statements of operations.

WARRANTY COSTS The Company provides currently for estimated future warranty and
installation costs on units sold covering the estimated replacement and
installation costs related to parts and labor.

METHODS OF RECORDING PROFITS ON CONTRACTS Revenues and profits are generally
recorded on cost reimbursement and long-term fixed-price contracts as costs are
incurred using the percentage-of-completion method. Percentages-of-completion
are determined by relating the actual cost of work performed to date for each
contract to its estimated final cost.


                                       32
<PAGE>   33
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998

Revenues and profits are recorded on other fixed price contracts as shipments
are made. Profit on fixed price contracts is determined by applying the
estimated average profit rate to the contract value of the items shipped. If a
loss is anticipated on a contract, provision is made at that time for the full
amount of the estimated loss without reference to the percentage of completion
or to performance milestones.

The types of milestones contained in contracts vary based on negotiations with
each customer, but may include acceptance of equipment prior to shipment,
shipment of equipment, arrival of equipment in the country, installation of
equipment and final customer acceptance. Individual customer deposits are
reduced by the amount of revenue recognized on the contract until a zero balance
is reached. Additional revenues earned in excess of a customer's deposit are
included in accounts receivable or unbilled costs and fees until paid or billed,
respectively.

Under the terms of most of its cost-reimbursement contracts, the Company is not
permitted to bill customers a specified portion of the contract value until
completion. Such retainages (approximately $856,000 in 1998 and $339,000 in
1997) result from both commercial contract retentions and government contract
withholdings generally for 15% of fees, as well as differences between the
actual and provisional indirect cost billing rates. Retainages are included in
the accompanying consolidated balance sheets as components of unbilled costs and
fees.

Included in accounts receivable and unbilled costs and fees at March 31, 1998
and March 28, 1997 are $8,098,000 and $3,694,000, respectively, attributable to
both prime and subcontracts with the U.S. Government.

WARRANTY COSTS AND DEFERRED REVENUE In general, the Company provides a one year
parts and labor warranty with the purchase of equipment. The anticipated cost
for this one year warranty is accrued for at time of sale and is captioned as a
balance sheet liability, Accrued Warranty. The Company also offers to its
customers extended warranty and service contracts beyond the initial year of
warranty. The coverage period of these contracts will typically range from one
to five years, with payment in advance recorded as Deferred Revenue.
Substantially all of the deferred revenue included in the accompanying 1998
balance sheet will be recognized within 2 years.

CUSTOMER DEPOSITS For most international orders, the Company attempts to
include, as part of its terms and conditions, an advance deposit with order
acceptance. For long-term international contracts, the Company will generally
include milestone payments tied to a specific event and/or passage of time.
These deposit amounts are recorded as a liability under "Customer Deposit" until
reduced by revenue recognized against the specific contract. As of March 31,
1998 and March 28, 1997, total customer deposits amounted to $1,151,000 and $0,
respectively.

DEFERRED RENT The Company entered into a lease for its office and manufacturing
facilities. This lease has escalation clauses. Generally accepted accounting
principles require normalization of the rental expense over the life of the
lease, resulting in deferred rent being reflected in the accompanying 1998
consolidated balance sheet.

RESEARCH AND DEVELOPMENT Research and development costs are expensed as
incurred.

FAIR VALUE OF FINANCIAL INSTRUMENTS The Company's financial instruments consist
primarily of cash and cash equivalents, accounts receivable and accounts
payable. The carrying amounts of the Company's cash and cash equivalents,
accounts receivable and accounts payable approximate fair value due to their
short-term nature.


                                       33
<PAGE>   34
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998

INCOME PER COMMON AND COMMON EQUIVALENT SHARES In March 1997, the Financial
Accounting Standards Board (FASB) issued Statement of Financial Accounting
Standards (SFAS) No. 128, "Earnings Per Share," which establishes standards for
computing and presenting earnings per share for entities with publicly held
common stock or potential common stock. The Company adopted SFAS 128 in fiscal
1998 and as required, restated per share amounts for all prior periods presented
to conform to the new requirements. Basic earnings per common share is computed
by dividing net income by the weighted average number of shares of common stock
outstanding during the year. No dilution for any potentially dilutive securities
is included. Diluted earnings per share includes the dilutive impact of options
and warrants using the average share price of the Company's common stock for the
period.

INCOME TAXES The Company accounts for incomes taxes in accordance with SFAS No.
109, "Accounting for Income Taxes." Accordingly, the Company recognizes deferred
income taxes based on the expected future tax consequences of differences
between the financial statement basis and the tax basis of assets and
liabilities, calculated using enacted tax rates in effect for the year in which
the differences are expected to be reflected in the tax return. The Company
records a valuation allowance against any net deferred tax assets if it is more
likely than not that they will not be realized.

NEW ACCOUNTING PRONOUNCEMENTS In February 1997, the FASB issued SFAS No. 129,
"Disclosure of Information about Capital Structure", which establishes standards
for disclosing information about an entity's capital structure. In June 1997,
the FASB issued SFAS No. 130, "Reporting Comprehensive Income", which
establishes standards for reporting and disclosure of comprehensive income and
its components (revenues, expenses, gains and losses) in a full set of general
purpose financial statements. Also, in June 1997, the FASB issued SFAS No. 131,
"Disclosures About Segments of an Enterprise and Related Information", which
establishes standards for reporting and disclosure of information about
operating segments as well as disclosures about products and services,
geographic areas and major customers. These statements are effective for fiscal
years beginning after December 15, 1997 and require certain additional
disclosures.

In April 1998, the AICPA Accounting Standards Executive Committee issued
Statement of Position No. 98-5 (SOP 98-5), "Reporting on the Costs of Start-Up
Activities", which is effective for fiscal years beginning after December 15,
1998. Early adoption is encouraged. SOP 98-5 requires that costs of start-up
activities and organization costs be expensed as incurred. The impact of
adopting SOP 98-5 will be accounted for as the cumulative effect of a change in
accounting principle as described in Accounting Principles Board Opinion No. 20,
"Accounting Changes". The Company does not anticipate any impact from adopting
SOP 98-5 as the Company currently expenses start-up and organization costs as
incurred.

PRESENTATION Certain amounts in 1997 and 1996 have been reclassified to conform
to the 1998 financial statement presentation.

2.  CASH AND CASH EQUIVALENTS

The Company considers all investments with original maturities of 90 days or
less to be cash equivalents. Cash and cash equivalents are carried at cost,
which approximates fair market value at year end 1998 and 1997. The Company has
repurchase agreements with a regional bank. The repurchase agreements are
collateralized by investments principally consisting of U.S. Government Agency
securities in the amount of at least 100% of such obligation.


                                       34
<PAGE>   35
            AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                MARCH 31, 1998

3.  OPERATING AND CAPITAL LEASE AGREEMENTS

In January 1995, the Company entered into a lease agreement for its new office
and manufacturing facilities in Billerica, Massachusetts. This lease has a term
of 10 years which started March 1, 1995, with an option to extend for 10
additional years. During fiscal year 1998 the Company leased additional space in
the current building and amended the lease. Escalation clauses provide for rent
increases after the first and fifth year of the rental term. In January 1998,
the Company leased additional manufacturing and office space at a nearby
location. This lease has a term of five years. The Company incurred $541,000,
$501,000, and $513,000 of rent expense in 1998, 1997, and 1996 respectively. The
security deposits on these leases amount to $106,000.

Future minimum rental payments under the Company's operating leases, excluding
real estate taxes, insurance and operating costs paid by the Company required
over the initial terms of the leases are as follows (in thousands):

<TABLE>
<CAPTION>
                          Year Ending March 31,
                          ---------------------
<S>                                       <C>
                         1999             $  590
                         2000                597
                         2001                681
                         2002                681
                         2003                662
                         Thereafter        1,159
                                          ------
                                          $4,370
                                          ======
</TABLE>


During fiscal 1995 the Company entered into a lease agreement for the purchase
of certain office equipment. This lease is classified as a capital lease under
generally accepted accounting principles and is payable in monthly installments
over a period of 60 months with interest of 11.5%. Future minimum lease payments
are as follows (in thousands):

<TABLE>
<CAPTION>
                         Year Ending March 31,
                         ---------------------
<S>                                                     <C>
          1999                                          $     24
          Thereafter                                          23
                                                        --------
          Total minimum lease payments                        47
          Less:  Amounts representing interest                (5)
                                                        --------
          Present value of net minimum
             lease payments                             $     42
                                                        ========
</TABLE>


                                       35
<PAGE>   36
            AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                MARCH 31, 1998

4.  LINE OF CREDIT

In August 1997, the Company renewed its domestic line with a regional bank,
increasing it from $2.5 million to $8.0 million. The renewed line of credit,
which is secured by accounts receivable from ongoing customers as well as
inventory, has two components. The first component is up to $4.0 million of base
borrowing capacity for either short term working capital borrowing or issuance
of standby letters of credit; the second component is an additional $4.0 million
in excess standby letters of credit capacity to support foreign equipment sales.
Monthly interest payments on this line of credit are at the prime interest rate.
There is a quarter percent (.25%) commitment fee on the unused portion of the
line. As of March 31, 1998 and March 28, 1997, there were no borrowings against
the line of credit, however, there were $1.2 million of outstanding letters of
credit in effect against this credit facility at March 31, 1998. During April
1998, the Company renegotiated the line of credit, dated August 1997, from $8
million to $12 million. The $12 million line of credit expires on August 31,
1998, at which time a formal credit renewal agreement is expected to be in
place. The Company's credit facility restricts the payment of dividends, except
in shares of the Company's stock, without consent of the bank.

5.  INCOME TAXES

The provision (benefit) for income taxes for the years ended March 31, 1998,
March 28, 1997, and March 29, 1996 consisted of the following (in thousands):

<TABLE>
<CAPTION>
                                      1998         1997         1996
                                    -------        -----        -----
<S>                                <C>            <C>          <C>
Current:
  Federal                           $    51        $  40        $  17
  State                                 353           38           13
                                    -------        -----        -----
                                        404           78           30
Deferred:
  Federal                             1,244          590          245
  State                                 (49)         112           49
                                    -------        -----        -----
                                      1,195          702          294
                                    -------        -----        -----
Change in valuation allowance        (3,562)        (702)        (294)
                                    -------        -----        -----
Total                               $(1,963)       $  78        $  30
                                    =======        =====        =====
</TABLE>

The difference between the total expected provision (benefit) for income taxes
computed by applying the statutory federal income tax rate to income before
provision (benefit) for income taxes and the recorded provision (benefit) for
income taxes for the three years in the period ended March 31, 1998 follows (in
thousands):

<TABLE>
<CAPTION>
                                                            1998         1997         1996
                                                         -------        -----        -----
<S>                                                      <C>            <C>          <C>
      Provision for income taxes at statutory rate       $   917        $ 681        $ 283
      State tax provision net of federal benefit             233           99           41
      Permanent non-deductible expenses                       17           17           17
      Expiration of tax credits                              190           --           --
      Change in valuation allowance                       (3,562)        (702)        (294)
      Alternative minimum tax                                 --           40           17
      Other                                                  242          (57)         (34)
                                                         -------        -----        -----
                                                         $(1,963)       $  78        $  30
                                                         =======        =====        =====
</TABLE>


                                       36
<PAGE>   37
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998

The significant components of the net deferred tax asset at March 31, 1998 and
March 28, 1997 follow (in thousands):

<TABLE>
<CAPTION>
                                                     1998                                1997
                                         ----------------------------        ----------------------------
                                             Current      Non-current            Current      Non-current
                                         ----------------------------        ----------------------------
<S>                                      <C>              <C>                <C>                <C>
ASSETS:
Net operating loss carryforwards         $     1,117      $         --       $         --       $   2,375
Accounts receivable
   and unbilled costs and fees                   259               --                238               --
Inventory                                        175               --                239               --
Deferred revenue                                 259               --                 --               --
Accrued vacation                                 136               --                 --               --
Accrued warranty costs                           194               --                114               --
Tax credits and other                            211              205                333              263
                                         -----------      -----------        -----------      -----------
                                               2,351              205                924            2,638

LESS:
Valuation allowance                               --               --               (924)          (2,638)
                                         -----------      -----------        -----------      -----------

Net deferred income tax assets             $   2,351      $       205        $         --     $        --
                                         ===========      ===========        ===========      ===========
</TABLE>

The change in the valuation allowance for the years ended March 31, 1998 and
March 28, 1997 follows (in thousands):

<TABLE>
<CAPTION>
                                                        1998           1997
                                                        ----           ----
<S>                                                  <C>           <C>
Valuation allowance, beginning of year               $  3,562      $    3,878
Decrease due to change in estimate of future
  taxable earnings                                     (3,562)           (316)
                                                     --------      ----------
Valuation allowance, end of year                     $     --      $    3,562
                                                     ========      ==========
</TABLE>

A valuation allowance is provided when it is more likely than not that some
portion of the net deferred tax asset will not be realized. All available
evidence, both positive and negative, is considered by management in forming a
conclusion regarding the need for a valuation allowance. Prior to 1998, the
Company maintained a full valuation allowance for net operating loss
carryforwards and other deferred tax amounts as a result of numerous negative
factors including the Company's history of recurring losses, the Company's
reliance on U.S. government agencies for sales, uncertainties related to the
cost of new business initiatives and ongoing litigation. In the fourth quarter
of 1998, management concluded that positive factors - consistent profitability,
revenue growth, improved competitive position and stable business operations -
outweighed negative factors. Based on these positive factors and the Company's
expected taxable income, the valuation allowance was reduced to zero with a
corresponding benefit recorded in the provision for income taxes for 1998.

At March 31, 1998, the Company had approximately $3,286,000 of federal net
operating loss carryforwards. The carryforwards expire through the year 2010.
The Company also has unused investment tax and other credits of approximately
$107,000 expiring through 2001.


                                       37
<PAGE>   38

              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998


6.  COMMON STOCK

STOCK OPTION PLANS The Company has various stock option plans for directors,
officers, and employees. During the year ended March 31, 1998, the Company
instituted two new common stock option plans, the 1998 and 1997 Non-Qualified
Stock Option Plans. These plans allow for grants of options in amounts
determined by a committee of the Board of Directors. The Company has the
following stock option plans outstanding as of March 31, 1998: 1966, 1968, 1970,
1981, 1984, 1985, and 1987 Stock Option Plans; 1993, 1994-1995 and 1996 Stock
Option Plan for Non-employee Directors; two CEO Employment Agreement Plans; 1995
Combination Plan; 1997 and 1998 Non-Qualified Option Plan; and 1994-95 Stock
Option Plan for New Employees. As of March 31, 1998, 1,318,154 shares have been
reserved and are available for future grant. Vesting periods on these plans
range from immediate vesting to four years. Options under these plans are
granted at fair market value and generally become exercisable within one to two
years of the grant date and terminate ten years from the date of grant. In
addition, the Company has a common stock installment purchase plan under which
the Board of Directors may grant to key personnel the right to purchase shares
of the Company's common stock at fair market value and to pay the purchase price
in twelve equal monthly installments. As of March 31, 1998, no shares have been
reserved or granted under this plan.

During the year ended March 28, 1997, the Company instituted two new common
stock purchase plans. The Executive Equity Incentive Plan allows an executive
officer of the Company to buy original issue Company common stock in any dollar
amount up to the gross amount of the annual bonus granted to the Officer and to
receive half the number of shares purchased in restricted stock. The Reload
Option Plan allows any eligible employee designated by the Board of Directors to
receive new stock options (at an exercise price equal to the fair market value
of the common stock on the date of sale of the stock) for every share of Company
common stock sold or used to exercise stock options.

PRO FORMA STOCK-BASED COMPENSATION EXPENSE In October 1995, the FASB issued SFAS
No. 123, "Accounting for Stock-Based Compensation," which sets forth a
fair-value based method of recognizing stock-based compensation expense. As
permitted by SFAS No. 123, the Company has elected to continue to apply
Accounting Principles Board Opinion No. 25, "Accounting for Stock Issued to
Employees," to account for its stock-based compensation plans. Had compensation
cost for awards in 1998, 1997 and 1996 under the Company's stock-based
compensation plans been determined based on the fair value at the grant dates
consistent with the method set forth under SFAS No. 123, the effect on the
Company's net income and earnings per share would have been as follows:


<TABLE>
<CAPTION>
In thousands except per share amounts            1998               1997               1996
                                               ---------         ----------         -----------
<S>                                           <C>               <C>                <C>         
Net income:
      As reported                             $    4,661        $     1,925        $        802
      Pro forma                                    3,200                591                 486
Income per share - Basic:
      As reported                             $     1.00        $       .43        $        .18
      Pro forma                                      .69                .13                 .11
Income per share - Diluted:
      As reported                             $      .95        $       .40        $        .18
      Pro forma                                      .65                .12                 .11

</TABLE>


                                       38
<PAGE>   39
             AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998

Because the method prescribed by SFAS No. 123 has not been applied to options
granted prior to April 1, 1995, the resulting pro forma compensation expense may
not be representative of the amount to be expensed in future years. Pro forma
compensation expense for options granted is reflected over the vesting period;
therefore, future pro forma compensation expense may be greater as additional
options are granted.

The fair value of each option granted was estimated on the grant date using the
Black-Scholes option pricing model with the following weighted average
assumptions: risk-free interest rates of 5.42% to 6.57%, 5.97% to 6.64%, 5.38%
to 6.24% for 1998, 1997, and 1996, respectively, and expected life of 5 years,
expected volatility of 38%, 30%, and 30% for 1998, 1997, and 1996, respectively,
and an expected dividend yield of 0% for all three years.


STOCK OPTION ACTIVITY A summary of the Company's stock option activity is as
follows:


<TABLE>
<CAPTION>
                                            1998                            1997                           1996
                                   ------------------------       -------------------------        -----------------------
                                                   Weighted                        Weighted                       Weighted
                                                    Average                         Average                        Average
                                   Number of       Exercise       Number of        Exercise        Number of      Exercise
                                      Shares          Price          Shares           Price           Shares         Price
                                      ------          -----          ------           -----           ------         -----
<S>                                <C>             <C>            <C>              <C>             <C>            <C>    
Options outstanding,
   beginning of year               1,001,141        $ 10.16         557,404         $  5.72          506,194       $  5.07
Options granted                      286,608          11.47         537,610           12.56          204,000          6.79
Options exercised                  (152,735)           5.79        (68,723)            5.32         (18,868)          4.67
Options expired                     (18,984)          10.99        (25,150)            8.06        (133,922)          5.93
                                    --------                       --------                        ---------

Options outstanding,
   end of year                     1,116,030           9.59       1,001,141           10.16          557,404          5.72
                                   =========                      =========                          =======

Options exercisable                  652,830           7.90         529,241            6.21          412,404          5.16
                                     =======                        =======                          =======

Options available
    for grant                      1,318,154                        681,538                          577,404
                                   =========                        =======                          =======

Weighted average fair
  value per share of
  options granted
  during the year                                      4.33                            4.24                           2.57
</TABLE>


                                       39
<PAGE>   40
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998


The following summarizes certain data for options outstanding at March 31, 1998:


<TABLE>
<CAPTION>
                                                                                             Weighted
                                                                           Weighted           Average
                                                                            Average         Remaining
                                 Number of                Range of         Exercise       Contractual
                                    Shares         Exercise Prices            Price              Life
                                    ------         ---------------            -----              ----
<S>                              <C>               <C>                   <C>              <C>
Options outstanding,
end of year:                       156,182         $2.88 - $  5.38       $     4.04              5.70
                                   236,609          5.38 -    7.88             6.02              6.40
                                   404,831          7.88 -   12.88            10.45              8.90
                                   318,408         12.88 -   16.25            13.86              8.70
                                 ---------
                                 1,116,030                                     9.59              7.80
                                 ---------

Options Exercisable:               156,182         $2.88 -  $ 5.38       $     4.04
                                   235,609          5.38 -    7.88             6.02
                                   136,631          7.88 -   12.88             9.99
                                   124,408         12.88 -   16.25            13.98
                                 ---------

                                   652,830                               $     7.90
                                 =========
</TABLE>


7. PRIVATE EQUITY PLACEMENT

During fiscal 1996 the Company, in a private placement, sold 203,044 shares of
common stock to a foreign investor for total consideration of $937,500. The
Company received net proceeds of $856,250. The Company utilized the services of
a financial services firm. As compensation, the financial services firm received
a fee of $81,250 as well as stock purchase warrants allowing the firm to
purchase up to 29,167 shares of the Company's stock at $6.25 per share. No
expense was recognized related to the issued warrants as the exercise price of
the warrants approximated fair value at the date of grant.


8.  EMPLOYMENT AGREEMENT AND NOTE RECEIVABLE FROM OFFICER

On January 12, 1994, the Company entered into an Employment Agreement with the
Company's President and Chief Executive Officer. On September 29, 1994, the
stockholders approved the issuance of non-qualified stock options for 80,000
shares (at $4.00 per share) to be exercised to varying extents at various times
through its expiration on December 16, 2003. The excess of the quoted market
price of the stock at the date of the award ($5.50) over the price stipulated by
the Agreement ($4.00) has been recognized by the Company as compensation
expense. This total amount has been amortized on a straight line basis over the
length of a vesting period of three years, through September 1997.

In addition, the Company's Chief Executive Officer purchased 160,000 shares of
common stock at a price of $4.00 per share (the fair market value) financed
under a note agreement for $640,000 from the Company. This note accrues interest
at a rate of 6.26% and will be payable on or before September 15, 2003 or 90
days after termination, as defined. As of March 31, 1998 no interest has been
received or paid against this note.

                                       40
<PAGE>   41
             AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998


9. RELATED PARTY TRANSACTIONS

The Company receives engineering and management consulting services from a
member of the Company's Board of Directors on a regular basis. In fiscal year
1998, 1997 and 1996 the Company paid approximately $256,750, $218,550, and
$160,800, for services rendered, respectively.


10.  BUSINESS SEGMENT INFORMATION

Certain financial information by business segment for the fiscal years 1998,
1997, and 1996 is presented below (dollars in thousands):


<TABLE>
<CAPTION>
                                                                     Depreciation       Net Sales            Income/
                                       Total          Capital             and         and Contract            (Loss)
Business Segment                      Assets        Expenditures     Amortization       Revenues            Before Tax
----------------                      ------        ------------     ------------       --------            ----------
<S>                                 <C>             <C>              <C>             <C>                  <C>         
1998
   X-ray Products                      $ 19,894        $   445         $  165        $        32,699       $      7,201
   Corporate                              6,099            637            369                     --             (4,599)

   Interest income                           --             --             --                     --                124
   Interest expense                          --             --             --                     --                 (6)
   Other expense, net                        --             --             --                     --                (22)
                                    -----------      ---------        -------        ---------------       ------------
                                    $    25,993      $   1,082        $   534        $        32,699       $      2,698
                                    ===========      =========        =======        ===============       ============


1997
   X-ray Products                   $    11,915      $     298        $   108        $        28,479       $      6,411
   Corporate                              3,599            432            244                     --             (4,451)

   Interest income                           --             --             --                     --                121
   Interest expense                          --             --             --                     --                (10)
   Other expense, net                        --             --             --                     --                (68)
                                    -----------      ---------        -------        ---------------       ------------
                                    $    15,514      $     730        $   352        $        28,479       $      2,003
                                    ===========      =========        =======        ===============       ============

1996
   X-ray Products                   $    10,081      $     163        $    50        $        17,815       $      4,385
   Corporate                              4,214             87            155                     --             (3,514)

   Interest income                           --             --             --                     --                131
   Interest expense                          --             --             --                     --                (79)
   Other expense, net                        --             --             --                     --                (91)
                                    -----------      ---------        -------        ---------------       ------------
                                    $    14,295      $     250        $   205        $        17,815       $        832
                                    ===========      =========        =======        ===============       ============
</TABLE>

Corporate assets consist primarily of cash and cash equivalents, prepaid
expenses and fixed assets.



                                       41
<PAGE>   42
             AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998


Approximately less than 1% of total revenues in 1998, 1997 and 1996,
respectively, were not related to X-ray products. Approximately 77% in 1998, 78%
in 1997, and 69% in 1996 of consolidated revenues were derived from prime and
subcontracts with, or sales to, various United States federal and state
governmental agencies.

Sales to major customers (representing in excess of 10% of consolidated sales)
consisted of X-ray Products segment sales of $11,670,000 to one customer in
1998, $11,531,000 and $3,463,000 to two customers, respectively, in 1997, and
$2,854,000 to one customer in 1996.

All of the Company's export sales originate from the U.S. No assets or
operations are maintained in any foreign country. The following table shows the
breakdown of Net Sales and Contract Revenues to foreign and domestic customers
and the major region(s) of export activity (dollars in thousands):


<TABLE>
<CAPTION>
                                                            1998           1997          1996
                                                            ----           ----          ----
<S>                                                  <C>             <C>           <C>       
Domestic                                             $    26,799     $   23,703    $   14,526
Export                                                     5,900          4,776         3,289
Percent of Export Revenue by Major Region:
    Middle East and Africa                                  59.7%          22.2%         20.9%
    Pacific Rim                                             28.3           60.9          39.2
    Europe                                                   8.9            4.4          24.4
    All Other                                                3.1           12.5           5.5
</TABLE>


11.  COMMITMENTS AND CONTINGENCIES

DEFERRED COMPENSATION The Company has an unfunded deferred compensation plan,
originally adopted in 1976 and amended at various times, for certain current and
former directors. This plan provides for periodic payments beginning at age 65,
the amount of which depends on their length of service. The Company paid $21,000
in 1998, $10,000 in 1997, and $21,000 in 1996 under this deferred compensation
plan.

LITIGATION In June 1997, the Company settled a suit and countersuit against the
Company's former Chief Executive Officer (the former CEO). As a result of the
settlement, the Company's ownership rights in certain technology were affirmed,
the Company gained rights to certain continuing developments made by the former
CEO's current company (Annistech), and the Company agreed to license that
technology back to Annistech.

In May, 1996, Vivid Technologies, Inc., filed a civil action against the
Company, seeking inter alia a declaratory judgment that Vivid had not infringed
upon certain of the Company patents relating to its backscatter technology. The
Company responded to Vivid's claim denying their allegations and
counter-claiming that Vivid infringed upon one or more of the Company's patents.
On May 12, 1997, Vivid filed a proposed Amended Complaint narrowing its claim
and seeking inter alia a declaratory judgment that Vivid had not infringed on
AS&E United States Patent number 5,253,283, entitled "Inspection Method and
Apparatus with Single Color Pixel Imaging." The Company denies Vivid's
assertions, and contends that Vivid's claims are without merit and that Vivid is
not entitled to the relief sought. The Company served Vivid with discovery
requests to which Vivid failed to respond. In September 1997, Vivid filed a
motion seeking a stay of discovery and a motion for a summary judgement. The
Company responded by seeking a denial or stay of Vivid's motion for summary
judgement until discovery could be completed. The Court denied the


                                       42
<PAGE>   43
             AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
                                 MARCH 31, 1998


Company's motion and declared that Vivid is not infringing on the patent. The
Company is currently appealing the Court's award of summary judgement and its
denial of discovery. The Company does not expect the outcome of this litigation
to have a material impact to its financial position or results of operations.

12.  SUBSEQUENT EVENT

On April 15, 1998, the Company announced that its Board of Directors adopted a
Shareholders' Rights Plan (the Plan) and declared a dividend of one preferred
stock purchase right for each outstanding share of common stock. The dividend is
payable to all holders of record of shares of common stock as of the close of
business on April 17, 1998. The rights become exercisable ten days after a
person or group acquires 15% or more of the Company's common stock, and in
certain other situations described in the Plan.


                                       43
<PAGE>   44
              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                 UNAUDITED QUARTERLY CONSOLIDATED FINANCIAL DATA
             FOR THE YEARS ENDED MARCH 31, 1998 AND MARCH 28, 1997

Dollars in thousands, except per share amounts


<TABLE>
<CAPTION>
                                          1998 BY QUARTER                                 1997 BY QUARTER
                                          ---------------                                 ---------------

                               1st        2nd        3rd        4th             1st        2nd        3rd        4th
                               ---        ---        ---        ---             ---        ---        ---        ---
<S>                        <C>        <C>        <C>        <C>            <C>         <C>        <C>        <C>    
Net sales and
contract revenues          $ 7,532    $ 8,705    $ 7,900    $ 8,562        $  6,699    $ 6,685    $ 7,127    $ 7,968

Gross profit                 2,750      3,521      3,208      3,404           2,091      2,356      2,832      2,777

Operating
income                         616        677        756        553             398        463        515        584

Net income                 $   610    $   685    $   751    $ 2,615(A)     $    406    $   451    $   503    $   565

Net income per share
    - Basic (Note 1)       $   .13    $   .15    $   .16    $   .55        $    .09    $   .10    $   .11    $   .12
    - Diluted (Note 1)         .13        .14        .15        .52             .09        .09        .10        .12
</TABLE>


(A) Includes an adjustment of approximately $2.1 million recorded in the fourth
    quarter of 1998 (Note 5) to recognize the tax benefit associated with
    federal net operating loss carryforwards, and certain other deferred tax
    assets.


                                       44
<PAGE>   45
                                                                     SCHEDULE II

              AMERICAN SCIENCE AND ENGINEERING, INC. AND SUBSIDIARY
                 VALUATION AND QUALIFYING ACCOUNTS AND RESERVES
     FOR THE YEARS ENDED MARCH 31, 1998, MARCH 28, 1997, AND MARCH 29, 1996


                        DESCRIPTION - ACCOUNTS RECEIVABLE

                              Dollars in thousands


<TABLE>
<CAPTION>
                Balance at       Charged to      Deductions        Balance
                Beginning         Costs and         from            at End
                 of Year          Expenses        Reserves         of Year
                 -------          --------        --------         -------
<S>             <C>              <C>             <C>              <C>    
1998            $   148           $     0         $     32        $   116

1997            $   179           $   178         $    209        $   148

1996            $    96           $   200         $    117        $   179
</TABLE>


DESCRIPTION - ALLOWANCES FOR UNBILLED COST AND FEES

Dollars in thousands


<TABLE>
<CAPTION>
                Balance at      Charged to       Deductions     Balance
                Beginning        Costs and          from         at End
                 of Year         Expenses         Reserves      of Year
                 -------         --------         --------      -------
<S>             <C>             <C>              <C>            <C>       
1998            $   462           $   200         $   113       $  549

1997            $    97           $   384         $    19       $  462

1996            $    72           $    25         $    --       $   97
</TABLE>


                                       45
<PAGE>   46
                                   SIGNATURES

Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, the Company has duly caused this report to be signed on its behalf
by the undersigned, thereunto duly authorized.

                                         AMERICAN SCIENCE AND ENGINEERING, INC.

DATED:   July 1998

                                         By  /s/ Ralph S. Sheridan
                                             --------------------------------
                                                 Ralph S. Sheridan, President

Pursuant to the requirements of the Securities Exchange Act of 1934, this report
has been signed below by the following persons on behalf of the Company and in
the capacities and on the dates indicated:

<TABLE>
<CAPTION>
Signature                                  Title                                  Date
---------                                  -----                                  ----
<S>                                        <C>                                  <C>
                                           President
/s/ Ralph S. Sheridan                      and Director (Principal
-------------------------------------      Executive Officer)
Ralph S. Sheridan                                                               13 July 1998


                                           
                                           Chief Financial Officer,     
                                           Treasurer and                
/s/ Lee C.  Steele                         Vice President, Finance              13 July 1998
-------------------------------------      (Principal Financial Officer)
Lee C. Steele                              


                                                                                13 July 1998
/s/ Joseph Moffa                           Controller                    
-------------------------------------      (Principal Accounting Officer)
Joseph Moffa                               


/s/ Herman Feshbach                        Chairman of the Board
-------------------------------------      of Directors
Herman Feshbach                                                                 13 July 1998


/s/  Al Gladen                             Director                             13 July 1998
-------------------------------------
Al Gladen


                                           Director                             13 July 1998
-------------------------------------
Hamilton W. Helmer


/s/ Donald J.  McCarren                    Director                             13 July 1998
-------------------------------------
Donald J. McCarren

/s/ William E. Odom                        Director                             13 July 1998
-------------------------------------
William E. Odom


/s/ Carl W. Vogt                           Director                             13 July 1998
-------------------------------------
Carl W. Vogt
</TABLE>


                                       46
<PAGE>   47
                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
Exhibit         Description of Exhibit (and Statement                                                     Page Number
Number          of Incorporation by Reference, If Applicable)                                             (If Filed)
------          ---------------------------------------------                                             ----------
<S>             <C>                                                                                       <C>     
(3)(a)          Restated Articles of Organization of the Company
                (filed as an Exhibit to Company's Annual Report on
                Form 10-K for the year ended September 30,
                1967, and incorporated herein by reference)

(3)(b)          Articles of Amendment to Restated Articles of Organization of Company
                (filed as Exhibit 2(a)(ii)(B) to the Company's Registration Statement on Form
                S-7,  No. 2-56452, filed May 25, 1976, and incorporated herein by
                reference)

(3)(c)          Articles of Amendment to Restated Articles of Organization of Company
                (filed as Exhibit 12 to the Company's Annual Report on Form 10-K for the
                year ended March 31, 1976, and incorporated herein by reference)

(3)(d)          By-laws of Company, as amended (filed as Exhibit 2(a)(iii) to Company's
                Registration Statement on Form S-7, No. 2-56452, filed May 25, 1976, and
                incorporated herein by reference)

(4)             Shareholders Rights Plan (filed as Exhibit  to the Company's filing on Form dated
                     , 1992 and incorporated herein by references)

(10)(a)(ii)     Deferred Compensation Plan for Herman Feshbach (filed as Exhibit 20 to the
                Company's Annual Report on Form 10-K for the year ended March 31, 1976,
                and incorporated herein by reference)

(10)(a)(iv)     Amendment to Deferred Compensation Plans for Ismael Escobar and Herman
                Feshbach (filed as Exhibit 7 to the Company's Annual Report on Form 10-K
                for the fiscal year ended March 31, 1980, and incorporated herein by
                reference)

(10)(a)(v)      Deferred Compensation Plan for Marie Spaulding (filed as
                Exhibit (10)(a)(v) to the Company's Annual Report on Form 10-K
                for the year ended March 31, 1988, and incorporated herein by
                reference)

(10)(b)(I)      1981 Incentive Stock Option Plan (filed as Exhibit (10)(b)(I)
                to the Company's Annual Report on Form 10-K for the year ended
                March 31, 1988, and incorporated herein by reference)

(10)(b)(iii)    1984 Incentive Stock Option Plan (filed as Exhibit (10)-3 to the Company's
                Annual Report on Form 10-K for the year ended March 31, 1985, and
                incorporated herein by reference)

(10)(b)(iv)     Amendment 1 to 1981 Incentive Stock Option Plan (filed as Exhibit
                (10)(b)(iv) to the Company's Annual Report on Form 10-K for the year ended
                March 31, 1988, and incorporated herein by reference)

(10)(b)(v)      Amendment 1 to 1984 Incentive Stock Option Plan (filed as
                Exhibit (10)(b)(v) to the Company's Annual Report on Form 10-K
                for the year ended March 31, 1988, and incorporated herein by
                reference)

(10)(b)(vi)     1987 General Stock Option Plan (filed as an exhibit to the Company's current
                report on Form 8-K for the month of October 1987, and incorporated herein
                by reference)

(10)(b)(vii)    Employment Agreement between the Company and Ralph S. Sheridan (dated
                as of September 26, 1996 filed herewith)                                                   49-55 
</TABLE>


                                       47
<PAGE>   48
<TABLE>
<CAPTION>
Exhibit         Description of Exhibit (and Statement                                                     Page Number
Number          of Incorporation by Reference, If Applicable)                                             (If Filed)
------          ---------------------------------------------                                             ----------
<S>             <C>                                                                                       <C>
(10)(b)(viii)   Loan and Security Agreement between the Company and Alfred
                Gladen as Agent (with forms of Promissory Note and Stock
                Purchase Warrants) (filed) as Exhibit 10(b)(vi) to the
                Company's Annual Report on Form 10-K for the year ended March
                31, 1995, and incorporated herein by reference)


(10)(b)(ix)     1996 Stock Plan For Non-Employee Directors (filed as Exhibit 99 to the
                Company's Registration Statement on Form S-8, File No. 333-09257,
                filed on July 31, 1996, and incorporated herein by reference)

(10)(b)(x)      Executive Equity Incentive Plan (filed as Exhibit 99 to the Company's
                Registration Statement on Form S-8, File No. 333-27929, filed on May 28,
                1997 and incorporated herein by reference)

(10)(b)(xi)     Reload Option Plan (filed as Exhibit (10)(b)(xi) to the
                Company's Annual Report on Form 10-K for the year ended March
                28, 1997 and incorporated herein by reference)

(10)(b)(xii)    1997 Non-Qualified Stock Option Plan (filed as Exhibit 99 to the Company's
                Registration Statement on Form S-8, File No. 333-27927, filed on
                May 28, 1997 and incorporated herein by reference)

(10)(b)(xiii)   1998 Non-Qualified Stock Option Plan, filed herewith                                        56-61

(10)(b)(xiv)    Employment Agreement between the Company and Jeffrey A. Bernfeld
                dated January 31, 1996, filed herewith                                                      62-65 

(10)(b)(xv)     Employment Agreement between the Company and Dr. Joseph Callerame
                dated May 6, 1998, filed herewith                                                           66-68

(10)(b)(xvi)    Employment Agreement between the Company and Alan H. Rutan
                dated June 4, 1996, filed herewith                                                          69-71 

(10)(b)(xvii)   Employment Agreement between the Company and Lee C. Steele
                dated September 29, 1997, filed herewith                                                    72-74

(10)(c)(i)      Lease of Billerica property (filed as Exhibit 10(c) to the
                Company's Annual Report on Form 10-K for the year ended March
                31, 1995 and incorporated herein by reference)

(10)(c)(ii)     Amendment to Lease of Billerica property (filed as to the
                Company's Annual Report on Form 10-K for the year ended March
                28, 1997 and incorporated herein by reference)

(22)            Identification of Company's subsidiary, AS&E Radiography, Inc.,
                incorporated in Massachusetts (filed as Exhibit (22) to Company's
                Annual Report on Form 10-K for the year ended March 31, 1988,
                and incorporated herein by reference)

(23)            Consent of Independent Public Accountants                                                      75 
</TABLE>


                                       48